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<!--Created on: 5/7/2026 2:14:16 PM-->
<!--Modified on: 5/7/2026 2:14:16 PM-->
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityShellCompany" xlink:to="dei_EntityShellCompany_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityShellCompany_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Entity Shell Company</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityShellCompany_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Entity Shell Company</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityExTransitionPeriod" xlink:to="dei_EntityExTransitionPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCommonStockSharesOutstanding" xlink:label="dei_EntityCommonStockSharesOutstanding" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityCommonStockSharesOutstanding" xlink:to="dei_EntityCommonStockSharesOutstanding_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCentralIndexKey" xlink:label="dei_EntityCentralIndexKey" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityCentralIndexKey" xlink:to="dei_EntityCentralIndexKey_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CurrentFiscalYearEndDate" xlink:label="dei_CurrentFiscalYearEndDate" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_CurrentFiscalYearEndDate" xlink:to="dei_CurrentFiscalYearEndDate_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentFiscalYearFocus" xlink:label="dei_DocumentFiscalYearFocus" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_DocumentFiscalYearFocus" xlink:to="dei_DocumentFiscalYearFocus_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_DocumentFiscalYearFocus_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Document Fiscal Year Focus</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentFiscalPeriodFocus" xlink:label="dei_DocumentFiscalPeriodFocus" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_DocumentFiscalPeriodFocus" xlink:to="dei_DocumentFiscalPeriodFocus_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_DocumentFiscalPeriodFocus_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Document Fiscal Period Focus</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AmendmentFlag" xlink:label="dei_AmendmentFlag" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_AmendmentFlag" xlink:to="dei_AmendmentFlag_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfFinancialPositionAbstract" xlink:label="us-gaap_StatementOfFinancialPositionAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementOfFinancialPositionAbstract" xlink:to="us-gaap_StatementOfFinancialPositionAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementOfFinancialPositionAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">CONSOLIDATED BALANCE SHEETS</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StatementOfFinancialPositionAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Balance Sheet</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementTable" xlink:label="us-gaap_StatementTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementTable" xlink:to="us-gaap_StatementTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Statement [Table]</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_SeriesaRedeemablePreferredStockMember" xlink:label="bhm_SeriesaRedeemablePreferredStockMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_SeriesaRedeemablePreferredStockMember" xlink:to="bhm_SeriesaRedeemablePreferredStockMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_SeriesaRedeemablePreferredStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Series A Redeemable Preferred Stock.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_SeriesaRedeemablePreferredStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SeriesA Redeemable Preferred Stock [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_SeriesaRedeemablePreferredStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Series A Redeemable Preferred Stock</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_SeriesBRedeemablePreferredStockMember" xlink:label="bhm_SeriesBRedeemablePreferredStockMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_SeriesBRedeemablePreferredStockMember" xlink:to="bhm_SeriesBRedeemablePreferredStockMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_SeriesBRedeemablePreferredStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Series B Redeemable Preferred Stock.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_SeriesBRedeemablePreferredStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Series B Redeemable Preferred Stock [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_SeriesBRedeemablePreferredStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Series B Redeemable Preferred Stock</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementLineItems" xlink:label="us-gaap_StatementLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_StatementLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Statement [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StatementLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Statement</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsAbstract" xlink:label="us-gaap_AssetsAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsAbstract" xlink:to="us-gaap_AssetsAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Assets [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AssetsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ASSETS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateInvestmentsAbstract" xlink:label="us-gaap_RealEstateInvestmentsAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RealEstateInvestmentsAbstract" xlink:to="us-gaap_RealEstateInvestmentsAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RealEstateInvestmentsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Real Estate Investments, Net [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_RealEstateInvestmentsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Real Estate Investments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Land" xlink:label="us-gaap_Land" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Land" xlink:to="us-gaap_Land_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Land_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Land</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_Land_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Land</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BuildingsAndImprovementsGross" xlink:label="us-gaap_BuildingsAndImprovementsGross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BuildingsAndImprovementsGross" xlink:to="us-gaap_BuildingsAndImprovementsGross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BuildingsAndImprovementsGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Buildings and Improvements, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_BuildingsAndImprovementsGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Buildings and improvements</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FurnitureAndFixturesGross" xlink:label="us-gaap_FurnitureAndFixturesGross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FurnitureAndFixturesGross" xlink:to="us-gaap_FurnitureAndFixturesGross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FurnitureAndFixturesGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Furniture and Fixtures, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FurnitureAndFixturesGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Furniture and fixtures</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_FurnitureAndFixturesGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Furniture, fixtures and equipment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConstructionInProgressGross" xlink:label="us-gaap_ConstructionInProgressGross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConstructionInProgressGross" xlink:to="us-gaap_ConstructionInProgressGross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConstructionInProgressGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Construction in Progress, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConstructionInProgressGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Construction in process</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateGrossAtCarryingValue" xlink:label="us-gaap_RealEstateGrossAtCarryingValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RealEstateGrossAtCarryingValue" xlink:to="us-gaap_RealEstateGrossAtCarryingValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RealEstateGrossAtCarryingValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SEC Schedule, 12-28, Real Estate Companies, Investment in Real Estate, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_RealEstateGrossAtCarryingValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total gross operating real estate investments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateAccumulatedDepreciation" xlink:label="us-gaap_RealEstateAccumulatedDepreciation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RealEstateAccumulatedDepreciation" xlink:to="us-gaap_RealEstateAccumulatedDepreciation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RealEstateAccumulatedDepreciation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SEC Schedule, 12-28, Real Estate Companies, Investment in Real Estate, Accumulated Depreciation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_RealEstateAccumulatedDepreciation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accumulated depreciation</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SECScheduleIIIRealEstateInvestmentPropertyNet" xlink:label="us-gaap_SECScheduleIIIRealEstateInvestmentPropertyNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SECScheduleIIIRealEstateInvestmentPropertyNet" xlink:to="us-gaap_SECScheduleIIIRealEstateInvestmentPropertyNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SECScheduleIIIRealEstateInvestmentPropertyNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SEC Schedule, 12-28, Real Estate Companies, Investment in Real Estate, Investment Property, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_SECScheduleIIIRealEstateInvestmentPropertyNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total net operating real estate investments</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_OperatingRealEstateLandHeldForSale" xlink:label="bhm_OperatingRealEstateLandHeldForSale" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_OperatingRealEstateLandHeldForSale" xlink:to="bhm_OperatingRealEstateLandHeldForSale_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_OperatingRealEstateLandHeldForSale_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of operating real estate land held for sale.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_OperatingRealEstateLandHeldForSale_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Real Estate, Land, Held-for-Sale</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_OperatingRealEstateLandHeldForSale_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating real estate held for sale, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateInvestments" xlink:label="us-gaap_RealEstateInvestments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RealEstateInvestments" xlink:to="us-gaap_RealEstateInvestments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RealEstateInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Real Estate Investments, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RealEstateInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net real estate assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_RealEstateInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total Net Real Estate Investments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:to="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and Cash Equivalents, at Carrying Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and cash equivalents</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and cash equivalents</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedCashAndCashEquivalents" xlink:label="us-gaap_RestrictedCashAndCashEquivalents" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RestrictedCashAndCashEquivalents" xlink:to="us-gaap_RestrictedCashAndCashEquivalents_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RestrictedCashAndCashEquivalents_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Restricted Cash and Cash Equivalents</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_RestrictedCashAndCashEquivalents_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Restricted cash</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestments" xlink:label="us-gaap_EquityMethodInvestments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityMethodInvestments" xlink:to="us-gaap_EquityMethodInvestments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityMethodInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EquityMethodInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment in unconsolidated real estate funds</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsAndOtherReceivablesNetCurrent" xlink:label="us-gaap_AccountsAndOtherReceivablesNetCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsAndOtherReceivablesNetCurrent" xlink:to="us-gaap_AccountsAndOtherReceivablesNetCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsAndOtherReceivablesNetCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts and Other Receivables, Net, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccountsAndOtherReceivablesNetCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts receivable, prepaids and other assets, net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AccountsAndOtherReceivablesNetCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts receivable, prepaids and other assets, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAfterAllowanceForCreditLoss" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAfterAllowanceForCreditLoss" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAfterAllowanceForCreditLoss" xlink:to="us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAfterAllowanceForCreditLoss_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAfterAllowanceForCreditLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Securities, Available-for-Sale, Amortized Cost, after Allowance for Credit Loss</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAfterAllowanceForCreditLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred equity investments, net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAfterAllowanceForCreditLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherIntangibleAssetsNet" xlink:label="us-gaap_OtherIntangibleAssetsNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherIntangibleAssetsNet" xlink:to="us-gaap_OtherIntangibleAssetsNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherIntangibleAssetsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Intangible Assets, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherIntangibleAssetsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other intangible assets, net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_OtherIntangibleAssetsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other intangible assets, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherReceivables" xlink:label="us-gaap_OtherReceivables" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherReceivables" xlink:to="us-gaap_OtherReceivables_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherReceivables_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Due from Affiliates</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherReceivables_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount receivable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_OtherReceivables_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Due from affiliates</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherReceivableAfterAllowanceForCreditLossRelatedPartyTypeExtensibleEnumeration" xlink:label="us-gaap_OtherReceivableAfterAllowanceForCreditLossRelatedPartyTypeExtensibleEnumeration" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherReceivableAfterAllowanceForCreditLossRelatedPartyTypeExtensibleEnumeration" xlink:to="us-gaap_OtherReceivableAfterAllowanceForCreditLossRelatedPartyTypeExtensibleEnumeration_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherReceivableAfterAllowanceForCreditLossRelatedPartyTypeExtensibleEnumeration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Receivable, after Allowance for Credit Loss, Related and Nonrelated Party Status [Extensible Enumeration]</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_NonRealEstateHeldForSale" xlink:label="bhm_NonRealEstateHeldForSale" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_NonRealEstateHeldForSale" xlink:to="bhm_NonRealEstateHeldForSale_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_NonRealEstateHeldForSale_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of investment associated with operating real estate held for sale. Excludes real estate assets.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_NonRealEstateHeldForSale_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non Real Estate, Held-for-Sale</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_NonRealEstateHeldForSale_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-real estate assets associated with operating real estate held for sale</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Assets" xlink:label="us-gaap_Assets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Assets" xlink:to="us-gaap_Assets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Assets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_Assets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">TOTAL ASSETS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities and Equity [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">LIABILITIES AND EQUITY</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtNoncurrent" xlink:label="us-gaap_LongTermDebtNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtNoncurrent" xlink:to="us-gaap_LongTermDebtNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermDebtNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-term Debt, Excluding Current Maturities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_LongTermDebtNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Mortgages payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsPayableCurrentAndNoncurrent" xlink:label="us-gaap_AccountsPayableCurrentAndNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsPayableCurrentAndNoncurrent" xlink:to="us-gaap_AccountsPayableCurrentAndNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsPayableCurrentAndNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AccountsPayableCurrentAndNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccruedLiabilitiesCurrentAndNoncurrent" xlink:label="us-gaap_AccruedLiabilitiesCurrentAndNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccruedLiabilitiesCurrentAndNoncurrent" xlink:to="us-gaap_AccruedLiabilitiesCurrentAndNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccruedLiabilitiesCurrentAndNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrued Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AccruedLiabilitiesCurrentAndNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other accrued liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherLiabilities" xlink:label="us-gaap_OtherLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherLiabilities" xlink:to="us-gaap_OtherLiabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Due to Affiliate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_OtherLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Due to affiliates</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherLiabilityRelatedPartyTypeExtensibleEnumeration" xlink:label="us-gaap_OtherLiabilityRelatedPartyTypeExtensibleEnumeration" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherLiabilityRelatedPartyTypeExtensibleEnumeration" xlink:to="us-gaap_OtherLiabilityRelatedPartyTypeExtensibleEnumeration_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherLiabilityRelatedPartyTypeExtensibleEnumeration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Liability, Related Party, Type [Extensible Enumeration]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DistributionPayable" xlink:label="us-gaap_DistributionPayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DistributionPayable" xlink:to="us-gaap_DistributionPayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DistributionPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Distributions Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DistributionPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Distributions payable</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_OperatingRealEstateHeldForSaleLiability" xlink:label="bhm_OperatingRealEstateHeldForSaleLiability" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_OperatingRealEstateHeldForSaleLiability" xlink:to="bhm_OperatingRealEstateHeldForSaleLiability_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_OperatingRealEstateHeldForSaleLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of liability associated with operating real estate held for sale.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_OperatingRealEstateHeldForSaleLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Real Estate, Held-for-Sale, Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_OperatingRealEstateHeldForSaleLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities associated with operating real estate held for sale</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Liabilities" xlink:label="us-gaap_Liabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Liabilities" xlink:to="us-gaap_Liabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:to="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stockholders' Equity, Including Portion Attributable to Noncontrolling Interest [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityAbstract" xlink:label="us-gaap_StockholdersEquityAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquityAbstract" xlink:to="us-gaap_StockholdersEquityAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stockholders' Equity Attributable to Parent [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockholdersEquityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stockholders' Equity</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockValue" xlink:label="us-gaap_PreferredStockValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockValue" xlink:to="us-gaap_PreferredStockValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PreferredStockValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Stock, Value, Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PreferredStockValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred stock, $0.01 par value, 206,000,000 shares authorized; no shares issued and outstanding at March 31, 2026 and December 31, 2025</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockValue" xlink:to="us-gaap_CommonStockValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdditionalPaidInCapital" xlink:label="us-gaap_AdditionalPaidInCapital" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdditionalPaidInCapital" xlink:to="us-gaap_AdditionalPaidInCapital_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AdditionalPaidInCapital_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional Paid in Capital</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AdditionalPaidInCapital_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional paid-in-capital</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RetainedEarningsAccumulatedDeficit" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RetainedEarningsAccumulatedDeficit" xlink:to="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Retained Earnings (Accumulated Deficit)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cumulative earnings in excess of distributions</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accumulated Other Comprehensive Income (Loss), Net of Tax</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accumulated other comprehensive gain</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquity" xlink:label="us-gaap_StockholdersEquity" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_StockholdersEquity_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stockholders' Equity Attributable to Parent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_StockholdersEquity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total Stockholders' Equity</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoncontrollingInterestItemsAbstract" xlink:label="us-gaap_NoncontrollingInterestItemsAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NoncontrollingInterestItemsAbstract" xlink:to="us-gaap_NoncontrollingInterestItemsAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NoncontrollingInterestItemsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling Interest Items [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NoncontrollingInterestItemsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling Interests</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterestInOperatingPartnerships" xlink:label="us-gaap_MinorityInterestInOperatingPartnerships" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MinorityInterestInOperatingPartnerships_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling Interest in Operating Partnerships</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MinorityInterestInOperatingPartnerships_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating partnership units</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_NoncontrollingInterestInPartiallyOwnedProperties" xlink:label="bhm_NoncontrollingInterestInPartiallyOwnedProperties" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_NoncontrollingInterestInPartiallyOwnedProperties" xlink:to="bhm_NoncontrollingInterestInPartiallyOwnedProperties_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_NoncontrollingInterestInPartiallyOwnedProperties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carrying amount of the equity interests owned by noncontrolling partners in partially owned properties included in the entity's consolidated financial statements.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_NoncontrollingInterestInPartiallyOwnedProperties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling Interest in Partially Owned Properties</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_NoncontrollingInterestInPartiallyOwnedProperties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Partially owned properties</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterest" xlink:label="us-gaap_MinorityInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MinorityInterest" xlink:to="us-gaap_MinorityInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MinorityInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stockholders' Equity Attributable to Noncontrolling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_MinorityInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total Noncontrolling Interests</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:to="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total Equity</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ending Balance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beginning Balance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total Equity</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAndStockholdersEquity" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities and Equity</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">TOTAL LIABILITIES AND EQUITY</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockDividendRatePercentage" xlink:label="us-gaap_PreferredStockDividendRatePercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PreferredStockDividendRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Stock, Dividend Rate, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PreferredStockDividendRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redeemable Preferred Stock, dividend rate (as a percent)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_PreferredStockDividendRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Dividend rate (as a percent)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityLiquidationPreferencePerShare" xlink:label="us-gaap_TemporaryEquityLiquidationPreferencePerShare" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquityLiquidationPreferencePerShare" xlink:to="us-gaap_TemporaryEquityLiquidationPreferencePerShare_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TemporaryEquityLiquidationPreferencePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Liquidation Preference Per Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TemporaryEquityLiquidationPreferencePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redeemable Preferred Stock, liquidation preference per share</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityParOrStatedValuePerShare" xlink:label="us-gaap_TemporaryEquityParOrStatedValuePerShare" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TemporaryEquityParOrStatedValuePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stated value per share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_TemporaryEquityParOrStatedValuePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redeemable Preferred Stock, stated value (in dollars per share)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquitySharesAuthorized" xlink:label="us-gaap_TemporaryEquitySharesAuthorized" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TemporaryEquitySharesAuthorized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redeemable Preferred Stock, shares authorized</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_TemporaryEquitySharesAuthorized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares authorized</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquitySharesIssued" xlink:label="us-gaap_TemporaryEquitySharesIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquitySharesIssued" xlink:to="us-gaap_TemporaryEquitySharesIssued_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TemporaryEquitySharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Shares Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TemporaryEquitySharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redeemable Preferred Stock, shares issued</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquitySharesOutstanding" xlink:label="us-gaap_TemporaryEquitySharesOutstanding" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquitySharesOutstanding" xlink:to="us-gaap_TemporaryEquitySharesOutstanding_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TemporaryEquitySharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Shares Outstanding</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_TemporaryEquitySharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ending balance (Shares)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_TemporaryEquitySharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beginning Balance (Shares)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TemporaryEquitySharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redeemable Preferred Stock, shares outstanding</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockParOrStatedValuePerShare" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockParOrStatedValuePerShare" xlink:to="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Stock, Par or Stated Value Per Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred stock, par value (in dollars per share)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockSharesAuthorized" xlink:label="us-gaap_PreferredStockSharesAuthorized" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockSharesAuthorized" xlink:to="us-gaap_PreferredStockSharesAuthorized_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Stock, Shares Authorized</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred stock, shares authorized</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockSharesIssued" xlink:label="us-gaap_PreferredStockSharesIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockSharesIssued" xlink:to="us-gaap_PreferredStockSharesIssued_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PreferredStockSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Stock, Shares Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PreferredStockSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred stock, shares issued</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockSharesOutstanding" xlink:label="us-gaap_PreferredStockSharesOutstanding" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockSharesOutstanding" xlink:to="us-gaap_PreferredStockSharesOutstanding_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Stock, Shares Outstanding</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred stock, shares outstanding</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockParOrStatedValuePerShare" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockParOrStatedValuePerShare" xlink:to="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Par or Stated Value Per Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock, par value (in dollars per share)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesAuthorized" xlink:label="us-gaap_CommonStockSharesAuthorized" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockSharesAuthorized" xlink:to="us-gaap_CommonStockSharesAuthorized_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Shares Authorized</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock, shares authorized</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesIssued" xlink:label="us-gaap_CommonStockSharesIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockSharesIssued" xlink:to="us-gaap_CommonStockSharesIssued_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Shares, Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock, shares issued</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesOutstanding" xlink:label="us-gaap_CommonStockSharesOutstanding" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockSharesOutstanding" xlink:to="us-gaap_CommonStockSharesOutstanding_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Shares, Outstanding</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock, shares outstanding</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementAbstract" xlink:label="us-gaap_IncomeStatementAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeStatementAbstract" xlink:to="us-gaap_IncomeStatementAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeStatementAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">CONSOLIDATED STATEMENTS OF OPERATIONS AND COMPREHENSIVE INCOME (LOSS)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeStatementAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Statement</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenuesAbstract" xlink:label="us-gaap_RevenuesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RevenuesAbstract" xlink:to="us-gaap_RevenuesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RevenuesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenues [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_RevenuesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenues</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueFromContractWithCustomerIncludingAssessedTax" xlink:label="us-gaap_RevenueFromContractWithCustomerIncludingAssessedTax" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RevenueFromContractWithCustomerIncludingAssessedTax" xlink:to="us-gaap_RevenueFromContractWithCustomerIncludingAssessedTax_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RevenueFromContractWithCustomerIncludingAssessedTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenue from Contract with Customer, Including Assessed Tax</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RevenueFromContractWithCustomerIncludingAssessedTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total rental and other property revenues</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_RevenueFromContractWithCustomerIncludingAssessedTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Rental and other property revenues</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestIncomeOperating" xlink:label="us-gaap_InterestIncomeOperating" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestIncomeOperating" xlink:to="us-gaap_InterestIncomeOperating_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InterestIncomeOperating_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Income, Operating</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InterestIncomeOperating_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest income from loan investments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_InterestIncomeOperating_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest income from loan investments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Revenues" xlink:label="us-gaap_Revenues" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Revenues" xlink:to="us-gaap_Revenues_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Revenues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenues</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_Revenues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total revenues</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CostsAndExpensesAbstract" xlink:label="us-gaap_CostsAndExpensesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CostsAndExpensesAbstract" xlink:to="us-gaap_CostsAndExpensesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CostsAndExpensesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Costs and Expenses [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CostsAndExpensesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Expenses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingCostsAndExpenses" xlink:label="us-gaap_OperatingCostsAndExpenses" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingCostsAndExpenses" xlink:to="us-gaap_OperatingCostsAndExpenses_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingCostsAndExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Costs and Expenses</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingCostsAndExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total property operating expenses</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_OperatingCostsAndExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property operating</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_PropertyManagementFeeExpense" xlink:label="bhm_PropertyManagementFeeExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_PropertyManagementFeeExpense" xlink:to="bhm_PropertyManagementFeeExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_PropertyManagementFeeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of expenses related to the managing property for management of the day-to-day business operations of the company.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_PropertyManagementFeeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property Management Fee Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="bhm_PropertyManagementFeeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property management and asset management fee expenses</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bhm_PropertyManagementFeeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property management and asset management fees</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GeneralAndAdministrativeExpense" xlink:label="us-gaap_GeneralAndAdministrativeExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GeneralAndAdministrativeExpense" xlink:to="us-gaap_GeneralAndAdministrativeExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">General and Administrative Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">General and administrative expenses</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">General and administrative</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_ManagementFeesRelatedParty" xlink:label="bhm_ManagementFeesRelatedParty" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_ManagementFeesRelatedParty" xlink:to="bhm_ManagementFeesRelatedParty_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_ManagementFeesRelatedParty_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of expense for management fees related party.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_ManagementFeesRelatedParty_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Management Fees Related Party</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="bhm_ManagementFeesRelatedParty_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Management fees to related party</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_ManagementFeesRelatedParty_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Management fees to related party</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AcquisitionCosts" xlink:label="us-gaap_AcquisitionCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AcquisitionCosts" xlink:to="us-gaap_AcquisitionCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AcquisitionCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquisition Costs, Period Cost</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_AcquisitionCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquisition and other transaction costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AcquisitionCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquisition and other transaction costs</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_LossFromCatastrophe" xlink:label="bhm_LossFromCatastrophe" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_LossFromCatastrophe" xlink:to="bhm_LossFromCatastrophe_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_LossFromCatastrophe_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of loss from catastrophes.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_LossFromCatastrophe_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss From Catastrophes</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_LossFromCatastrophe_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weather-related losses, net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bhm_LossFromCatastrophe_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weather-related losses, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ImpairmentOfRealEstate" xlink:label="us-gaap_ImpairmentOfRealEstate" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ImpairmentOfRealEstate" xlink:to="us-gaap_ImpairmentOfRealEstate_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ImpairmentOfRealEstate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Impairment of Real Estate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_ImpairmentOfRealEstate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total impairments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ImpairmentOfRealEstate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Impairment of real estate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ImpairmentOfRealEstate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Impairment of real estate investments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DepreciationAndAmortization" xlink:label="us-gaap_DepreciationAndAmortization" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DepreciationAndAmortization" xlink:to="us-gaap_DepreciationAndAmortization_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DepreciationAndAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Depreciation, Depletion and Amortization, Nonproduction</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_DepreciationAndAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Depreciation and amortization</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DepreciationAndAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Depreciation and amortization</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingExpenses" xlink:label="us-gaap_OperatingExpenses" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingExpenses" xlink:to="us-gaap_OperatingExpenses_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Expenses</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_OperatingExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total expenses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NonoperatingIncomeExpenseAbstract" xlink:label="us-gaap_NonoperatingIncomeExpenseAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NonoperatingIncomeExpenseAbstract" xlink:to="us-gaap_NonoperatingIncomeExpenseAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NonoperatingIncomeExpenseAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Nonoperating Income (Expense) [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_NonoperatingIncomeExpenseAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other (expense) income</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherNonoperatingIncomeExpense" xlink:label="us-gaap_OtherNonoperatingIncomeExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherNonoperatingIncomeExpense" xlink:to="us-gaap_OtherNonoperatingIncomeExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherNonoperatingIncomeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Nonoperating Income (Expense)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherNonoperatingIncomeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other expense, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromEquityMethodInvestments" xlink:label="us-gaap_IncomeLossFromEquityMethodInvestments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeLossFromEquityMethodInvestments" xlink:to="us-gaap_IncomeLossFromEquityMethodInvestments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeLossFromEquityMethodInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income (Loss) from Equity Method Investments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_IncomeLossFromEquityMethodInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income from preferred equity investments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeLossFromEquityMethodInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total income from preferred equity investments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_IncomeLossFromEquityMethodInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income from preferred equity investments</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_IncomeFromInvestmentsInUnconsolidatedRealEstateFunds" xlink:label="bhm_IncomeFromInvestmentsInUnconsolidatedRealEstateFunds" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_IncomeFromInvestmentsInUnconsolidatedRealEstateFunds" xlink:to="bhm_IncomeFromInvestmentsInUnconsolidatedRealEstateFunds_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_IncomeFromInvestmentsInUnconsolidatedRealEstateFunds_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of income (loss) from unconsolidated real estate investments fund attributed to parent.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_IncomeFromInvestmentsInUnconsolidatedRealEstateFunds_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income From Investments In Unconsolidated Real Estate Funds</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="bhm_IncomeFromInvestmentsInUnconsolidatedRealEstateFunds_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share of net earnings of equity method investment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_IncomeFromInvestmentsInUnconsolidatedRealEstateFunds_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income from investments in unconsolidated real estate funds</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bhm_IncomeFromInvestmentsInUnconsolidatedRealEstateFunds_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share of net earnings of equity method investment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivablePeriodIncreaseDecrease" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivablePeriodIncreaseDecrease" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AllowanceForDoubtfulAccountsReceivablePeriodIncreaseDecrease" xlink:to="us-gaap_AllowanceForDoubtfulAccountsReceivablePeriodIncreaseDecrease_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivablePeriodIncreaseDecrease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable, Allowance for Credit Loss, Period Increase (Decrease)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivablePeriodIncreaseDecrease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Recovery of credit losses, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnSaleOfInvestments" xlink:label="us-gaap_GainLossOnSaleOfInvestments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GainLossOnSaleOfInvestments" xlink:to="us-gaap_GainLossOnSaleOfInvestments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GainLossOnSaleOfInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (Loss) on Sale of Investments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_GainLossOnSaleOfInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain on sale of real estate investments, net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GainLossOnSaleOfInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain on sale of real estate investments, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:to="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (Loss) on Extinguishment of Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on extinguishment of debt costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on extinguishment of debt costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on extinguishment of debt</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestIncomeExpenseNonoperatingNet" xlink:label="us-gaap_InterestIncomeExpenseNonoperatingNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestIncomeExpenseNonoperatingNet" xlink:to="us-gaap_InterestIncomeExpenseNonoperatingNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InterestIncomeExpenseNonoperatingNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Income (Expense), Nonoperating, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_InterestIncomeExpenseNonoperatingNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest expense, net</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_InterestIncome" xlink:label="bhm_InterestIncome" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_InterestIncome" xlink:to="bhm_InterestIncome_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_InterestIncome_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount before accretion (amortization) of purchase discount (premium) of interest income on nonoperating securities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_InterestIncome_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Income</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_InterestIncome_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest income</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NonoperatingIncomeExpense" xlink:label="us-gaap_NonoperatingIncomeExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NonoperatingIncomeExpense" xlink:to="us-gaap_NonoperatingIncomeExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NonoperatingIncomeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Nonoperating Income (Expense)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NonoperatingIncomeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total other expense</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:to="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:to="us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Comprehensive Income (Loss), Net of Tax, Attributable to Noncontrolling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Comprehensive loss attributable to noncontrolling interests</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComprehensiveIncomeNetOfTax" xlink:label="us-gaap_ComprehensiveIncomeNetOfTax" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ComprehensiveIncomeNetOfTax" xlink:to="us-gaap_ComprehensiveIncomeNetOfTax_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ComprehensiveIncomeNetOfTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_ComprehensiveIncomeNetOfTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Comprehensive loss attributable to common stockholders</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_StatementsOfNetParentInvestment" xlink:label="bhm_StatementsOfNetParentInvestment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_StatementsOfNetParentInvestment" xlink:to="bhm_StatementsOfNetParentInvestment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_StatementsOfNetParentInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">No definition available.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_StatementsOfNetParentInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">CONSOLIDATED STATEMENTS OF STOCKHOLDERS' EQUITY</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementEquityComponentsAxis" xlink:label="us-gaap_StatementEquityComponentsAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementEquityComponentsAxis" xlink:to="us-gaap_StatementEquityComponentsAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementEquityComponentsAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Components [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityComponentDomain" xlink:label="us-gaap_EquityComponentDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityComponentDomain" xlink:to="us-gaap_EquityComponentDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityComponentDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Component [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockMember" xlink:label="us-gaap_CommonStockMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockMember" xlink:to="us-gaap_CommonStockMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdditionalPaidInCapitalMember" xlink:label="us-gaap_AdditionalPaidInCapitalMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdditionalPaidInCapitalMember" xlink:to="us-gaap_AdditionalPaidInCapitalMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AdditionalPaidInCapitalMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional Paid-in Capital [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AdditionalPaidInCapitalMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional Paid-in Capital</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedDistributionsInExcessOfNetIncomeMember" xlink:label="us-gaap_AccumulatedDistributionsInExcessOfNetIncomeMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccumulatedDistributionsInExcessOfNetIncomeMember" xlink:to="us-gaap_AccumulatedDistributionsInExcessOfNetIncomeMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccumulatedDistributionsInExcessOfNetIncomeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cumulative Distributions [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccumulatedDistributionsInExcessOfNetIncomeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cumulative Earnings</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:to="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">AOCI Attributable to Parent [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accumulated Other Comprehensive (Loss) Income</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoncontrollingInterestMember" xlink:label="us-gaap_NoncontrollingInterestMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NoncontrollingInterestMember" xlink:to="us-gaap_NoncontrollingInterestMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NoncontrollingInterestMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling Interests [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NoncontrollingInterestMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling Interests</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_StockIssuedDuringPeriodValueIssuanceOfRestrictedStockAndLtipUnitsForEquityIncentivePlanCompensationNetOfSharesWithheldForEmployeeTaxes" xlink:label="bhm_StockIssuedDuringPeriodValueIssuanceOfRestrictedStockAndLtipUnitsForEquityIncentivePlanCompensationNetOfSharesWithheldForEmployeeTaxes" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_StockIssuedDuringPeriodValueIssuanceOfRestrictedStockAndLtipUnitsForEquityIncentivePlanCompensationNetOfSharesWithheldForEmployeeTaxes" xlink:to="bhm_StockIssuedDuringPeriodValueIssuanceOfRestrictedStockAndLtipUnitsForEquityIncentivePlanCompensationNetOfSharesWithheldForEmployeeTaxes_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_StockIssuedDuringPeriodValueIssuanceOfRestrictedStockAndLtipUnitsForEquityIncentivePlanCompensationNetOfSharesWithheldForEmployeeTaxes_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of issuance of restricted Class A common stock and LTIP Units for equity incentive plan compensation net of shares withheld for employee taxes.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_StockIssuedDuringPeriodValueIssuanceOfRestrictedStockAndLtipUnitsForEquityIncentivePlanCompensationNetOfSharesWithheldForEmployeeTaxes_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Value, Issuance of Restricted Stock and LTIP Units for Equity Incentive Plan Compensation, Net of Shares Withheld for Employee Taxes</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_StockIssuedDuringPeriodValueIssuanceOfRestrictedStockAndLtipUnitsForEquityIncentivePlanCompensationNetOfSharesWithheldForEmployeeTaxes_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">(Forfeiture) issuance of restricted Class A common stock for equity incentive plan compensation</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_StockIssuedDuringPeriodSharesIssuanceOfRestrictedStockAndLtipUnitsForEquityIncentivePlanCompensationNetOfSharesWithheldForEmployeeTaxes" xlink:label="bhm_StockIssuedDuringPeriodSharesIssuanceOfRestrictedStockAndLtipUnitsForEquityIncentivePlanCompensationNetOfSharesWithheldForEmployeeTaxes" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_StockIssuedDuringPeriodSharesIssuanceOfRestrictedStockAndLtipUnitsForEquityIncentivePlanCompensationNetOfSharesWithheldForEmployeeTaxes" xlink:to="bhm_StockIssuedDuringPeriodSharesIssuanceOfRestrictedStockAndLtipUnitsForEquityIncentivePlanCompensationNetOfSharesWithheldForEmployeeTaxes_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_StockIssuedDuringPeriodSharesIssuanceOfRestrictedStockAndLtipUnitsForEquityIncentivePlanCompensationNetOfSharesWithheldForEmployeeTaxes_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The shares issued during the period for issuance of restricted Class A common stock and LTIP Units for equity incentive plan compensation net of shares withheld for employee taxes.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_StockIssuedDuringPeriodSharesIssuanceOfRestrictedStockAndLtipUnitsForEquityIncentivePlanCompensationNetOfSharesWithheldForEmployeeTaxes_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Issuance of Restricted Stock and LTIP Units for Equity Incentive Plan Compensation, Net of Shares Withheld for Employee Taxes</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_StockIssuedDuringPeriodSharesIssuanceOfRestrictedStockAndLtipUnitsForEquityIncentivePlanCompensationNetOfSharesWithheldForEmployeeTaxes_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">(Forfeiture) issuance of restricted Class A common stock for equity incentive plan compensation (Shares)</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_NoncontrollingInterestIncreaseFromIssuanceOfLtipUnitsForEquityIncentivePlanCompensationNetOfForfeitures" xlink:label="bhm_NoncontrollingInterestIncreaseFromIssuanceOfLtipUnitsForEquityIncentivePlanCompensationNetOfForfeitures" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_NoncontrollingInterestIncreaseFromIssuanceOfLtipUnitsForEquityIncentivePlanCompensationNetOfForfeitures" xlink:to="bhm_NoncontrollingInterestIncreaseFromIssuanceOfLtipUnitsForEquityIncentivePlanCompensationNetOfForfeitures_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_NoncontrollingInterestIncreaseFromIssuanceOfLtipUnitsForEquityIncentivePlanCompensationNetOfForfeitures_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of increase in non-controlling interest from issuance of LTIP Units for equity incentive plan compensation net of forfeitures.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_NoncontrollingInterestIncreaseFromIssuanceOfLtipUnitsForEquityIncentivePlanCompensationNetOfForfeitures_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling Interest, Increase From Issuance Of Ltip Units For Equity Incentive Plan Compensation, Net Of Forfeitures</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_NoncontrollingInterestIncreaseFromIssuanceOfLtipUnitsForEquityIncentivePlanCompensationNetOfForfeitures_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of long-term incentive plan ("LTIP") Units for equity incentive plan compensation</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_NoncontrollingInterestIncreaseFromIssuanceOfLtipUnitsForEquityIncentivePlanCompensation" xlink:label="bhm_NoncontrollingInterestIncreaseFromIssuanceOfLtipUnitsForEquityIncentivePlanCompensation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_NoncontrollingInterestIncreaseFromIssuanceOfLtipUnitsForEquityIncentivePlanCompensation" xlink:to="bhm_NoncontrollingInterestIncreaseFromIssuanceOfLtipUnitsForEquityIncentivePlanCompensation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_NoncontrollingInterestIncreaseFromIssuanceOfLtipUnitsForEquityIncentivePlanCompensation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of increase in non-controlling interest from issuance of LTIP Units for equity incentive plan compensation.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_NoncontrollingInterestIncreaseFromIssuanceOfLtipUnitsForEquityIncentivePlanCompensation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling Interest, Increase From Issuance Of Ltip Units For Equity Incentive Plan Compensation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_NoncontrollingInterestIncreaseFromIssuanceOfLtipUnitsForEquityIncentivePlanCompensation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of LTIP Units for equity incentive plan compensation</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_StockIssuedDuringPeriodValueIssuanceOfLtipUnitsToManager" xlink:label="bhm_StockIssuedDuringPeriodValueIssuanceOfLtipUnitsToManager" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_StockIssuedDuringPeriodValueIssuanceOfLtipUnitsToManager" xlink:to="bhm_StockIssuedDuringPeriodValueIssuanceOfLtipUnitsToManager_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_StockIssuedDuringPeriodValueIssuanceOfLtipUnitsToManager_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Value of shares of stock issued during the period for issuance of LTIP Units to Manager.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_StockIssuedDuringPeriodValueIssuanceOfLtipUnitsToManager_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period Value, Issuance of LTIP Units to Manager</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_StockIssuedDuringPeriodValueIssuanceOfLtipUnitsToManager_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of C-LTIP Units to Bluerock Homes Manager, LLC ("Manager")</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DividendsCommonStock" xlink:label="us-gaap_DividendsCommonStock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DividendsCommonStock" xlink:to="us-gaap_DividendsCommonStock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DividendsCommonStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Dividends, Common Stock</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_DividendsCommonStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock distributions declared</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DividendsPreferredStock" xlink:label="us-gaap_DividendsPreferredStock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DividendsPreferredStock" xlink:to="us-gaap_DividendsPreferredStock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DividendsPreferredStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Dividends, Preferred Stock</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_DividendsPreferredStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Stock distributions declared</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_DecreaseFromDistributionsToOperatingPartnershipNoncontrollingInterestHolders" xlink:label="bhm_DecreaseFromDistributionsToOperatingPartnershipNoncontrollingInterestHolders" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_DecreaseFromDistributionsToOperatingPartnershipNoncontrollingInterestHolders" xlink:to="bhm_DecreaseFromDistributionsToOperatingPartnershipNoncontrollingInterestHolders_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_DecreaseFromDistributionsToOperatingPartnershipNoncontrollingInterestHolders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Decrease in noncontrolling interest balance from payment of dividends or other distributions by the non-wholly owned subsidiary or partially owned entity, included in the consolidation of the parent entity, to the noncontrolling interest holders.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_DecreaseFromDistributionsToOperatingPartnershipNoncontrollingInterestHolders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Decrease From Distributions To Operating Partnership Noncontrolling Interest Holders</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="bhm_DecreaseFromDistributionsToOperatingPartnershipNoncontrollingInterestHolders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Distributions to Operating Partnership noncontrolling interests</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders" xlink:label="us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders" xlink:to="us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling Interest, Decrease from Distributions to Noncontrolling Interest Holders</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Distributions to partially owned properties' noncontrolling interests</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_NonControllingInterestIncreaseFromContributions" xlink:label="bhm_NonControllingInterestIncreaseFromContributions" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_NonControllingInterestIncreaseFromContributions" xlink:to="bhm_NonControllingInterestIncreaseFromContributions_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_NonControllingInterestIncreaseFromContributions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of increase in noncontrolling interest from contributions.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_NonControllingInterestIncreaseFromContributions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non Controlling Interest, Increase From Contributions</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_NonControllingInterestIncreaseFromContributions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contributions from noncontrolling interests</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:label="us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:to="us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Conversion of Convertible Securities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares issued in conversion (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalIncreaseInCarryingAmountOfRedeemablePreferredStock" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalIncreaseInCarryingAmountOfRedeemablePreferredStock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdjustmentsToAdditionalPaidInCapitalIncreaseInCarryingAmountOfRedeemablePreferredStock" xlink:to="us-gaap_AdjustmentsToAdditionalPaidInCapitalIncreaseInCarryingAmountOfRedeemablePreferredStock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalIncreaseInCarryingAmountOfRedeemablePreferredStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustments to Additional Paid in Capital, Increase in Carrying Amount of Redeemable Preferred Stock</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalIncreaseInCarryingAmountOfRedeemablePreferredStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash redemption of Series A Preferred Stock</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_AdjustmentForNoncontrollingInterestOwnershipInOperatingPartnership" xlink:label="bhm_AdjustmentForNoncontrollingInterestOwnershipInOperatingPartnership" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_AdjustmentForNoncontrollingInterestOwnershipInOperatingPartnership" xlink:to="bhm_AdjustmentForNoncontrollingInterestOwnershipInOperatingPartnership_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_AdjustmentForNoncontrollingInterestOwnershipInOperatingPartnership_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of adjustment for noncontrolling interest ownership in operating partnership.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_AdjustmentForNoncontrollingInterestOwnershipInOperatingPartnership_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustment for Noncontrolling Interest Ownership In Operating Partnership</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="bhm_AdjustmentForNoncontrollingInterestOwnershipInOperatingPartnership_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustment for noncontrolling interest ownership in the Operating Partnership</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_NoncontrollingInterestIncreaseDecreaseInPartiallyOwnedProperties" xlink:label="bhm_NoncontrollingInterestIncreaseDecreaseInPartiallyOwnedProperties" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_NoncontrollingInterestIncreaseDecreaseInPartiallyOwnedProperties" xlink:to="bhm_NoncontrollingInterestIncreaseDecreaseInPartiallyOwnedProperties_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_NoncontrollingInterestIncreaseDecreaseInPartiallyOwnedProperties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of increase (decrease) in noncontrolling interest of partially owned properties.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_NoncontrollingInterestIncreaseDecreaseInPartiallyOwnedProperties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling Interest, Increase (Decrease) in Partially Owned Properties</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_NoncontrollingInterestIncreaseDecreaseInPartiallyOwnedProperties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustment for noncontrolling interest ownership in partially owned properties</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfCashFlowsAbstract" xlink:label="us-gaap_StatementOfCashFlowsAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementOfCashFlowsAbstract" xlink:to="us-gaap_StatementOfCashFlowsAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementOfCashFlowsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">CONSOLIDATED STATEMENTS OF CASH FLOWS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Cash Provided by (Used in) Operating Activities [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash flows from operating activities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustments to Reconcile Net Income (Loss) to Cash Provided by (Used in) Operating Activities [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustments to reconcile net loss to net cash provided by operating activities:</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_DepreciationAndAmortizationExcludingAmortizationOfDebtDiscountOrPremium" xlink:label="bhm_DepreciationAndAmortizationExcludingAmortizationOfDebtDiscountOrPremium" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_DepreciationAndAmortizationExcludingAmortizationOfDebtDiscountOrPremium" xlink:to="bhm_DepreciationAndAmortizationExcludingAmortizationOfDebtDiscountOrPremium_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_DepreciationAndAmortizationExcludingAmortizationOfDebtDiscountOrPremium_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The aggregate expense recognized in the current period that allocates the cost of tangible assets, intangible assets, or depleting assets to periods that benefit from use of the assets, excluding amortization of debt discount or premium, which is reported separately.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_DepreciationAndAmortizationExcludingAmortizationOfDebtDiscountOrPremium_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Depreciation And Amortization Excluding Amortization Of Debt Discount Or Premium</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_DepreciationAndAmortizationExcludingAmortizationOfDebtDiscountOrPremium_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Depreciation and amortization</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AmortizationOfDebtDiscountPremium" xlink:label="us-gaap_AmortizationOfDebtDiscountPremium" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AmortizationOfDebtDiscountPremium" xlink:to="us-gaap_AmortizationOfDebtDiscountPremium_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AmortizationOfDebtDiscountPremium_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amortization of Debt Discount (Premium)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AmortizationOfDebtDiscountPremium_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amortization of fair value adjustments</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_FairValueAdjustmentOfInterestRateCaps" xlink:label="bhm_FairValueAdjustmentOfInterestRateCaps" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_FairValueAdjustmentOfInterestRateCaps" xlink:to="bhm_FairValueAdjustmentOfInterestRateCaps_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_FairValueAdjustmentOfInterestRateCaps_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of expense (income) related to adjustment to fair value of interest rate caps.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_FairValueAdjustmentOfInterestRateCaps_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Adjustment Of Interest Rate Caps</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bhm_FairValueAdjustmentOfInterestRateCaps_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value adjustment of interest rate caps and swaps</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProvisionForDoubtfulAccounts" xlink:label="us-gaap_ProvisionForDoubtfulAccounts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProvisionForDoubtfulAccounts" xlink:to="us-gaap_ProvisionForDoubtfulAccounts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProvisionForDoubtfulAccounts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable, Credit Loss Expense (Reversal)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProvisionForDoubtfulAccounts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Recovery of credit losses, net</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_NoncashOperatingLeaseExpense" xlink:label="bhm_NoncashOperatingLeaseExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_NoncashOperatingLeaseExpense" xlink:to="bhm_NoncashOperatingLeaseExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_NoncashOperatingLeaseExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of noncash operating lease expense.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_NoncashOperatingLeaseExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncash Operating Lease Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_NoncashOperatingLeaseExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncash operating lease expense</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_ProceedsFromPreferredEquityInvestmentDistribution" xlink:label="bhm_ProceedsFromPreferredEquityInvestmentDistribution" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_ProceedsFromPreferredEquityInvestmentDistribution" xlink:to="bhm_ProceedsFromPreferredEquityInvestmentDistribution_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_ProceedsFromPreferredEquityInvestmentDistribution_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of distribution received from preferred equity investments classified as operating activities. Excludes distribution for return of investment, classified as investing activities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_ProceedsFromPreferredEquityInvestmentDistribution_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Preferred Equity Investment, Distribution</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_ProceedsFromPreferredEquityInvestmentDistribution_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Distributions of income from preferred equity investments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentDividendsOrDistributions" xlink:label="us-gaap_EquityMethodInvestmentDividendsOrDistributions" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityMethodInvestmentDividendsOrDistributions" xlink:to="us-gaap_EquityMethodInvestmentDividendsOrDistributions_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityMethodInvestmentDividendsOrDistributions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Equity Method Investment, Distribution</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_EquityMethodInvestmentDividendsOrDistributions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Distributions from investments in unconsolidated real estate funds</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_AdjustmentsForShareBasedPaymentsAttributableToEquityIncentivePlan" xlink:label="bhm_AdjustmentsForShareBasedPaymentsAttributableToEquityIncentivePlan" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_AdjustmentsForShareBasedPaymentsAttributableToEquityIncentivePlan" xlink:to="bhm_AdjustmentsForShareBasedPaymentsAttributableToEquityIncentivePlan_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_AdjustmentsForShareBasedPaymentsAttributableToEquityIncentivePlan_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustments for share-based compensation attributable to equity incentive plan to reconcile profit (loss) to net cash flow from (used in) operating activities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_AdjustmentsForShareBasedPaymentsAttributableToEquityIncentivePlan_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustments for Share-based Payments Attributable to Equity Incentive Plan</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_AdjustmentsForShareBasedPaymentsAttributableToEquityIncentivePlan_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-based compensation attributable to equity incentive plan</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_AdjustmentsForShareBasedPaymentsAttributableToLtipUnits" xlink:label="bhm_AdjustmentsForShareBasedPaymentsAttributableToLtipUnits" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_AdjustmentsForShareBasedPaymentsAttributableToLtipUnits" xlink:to="bhm_AdjustmentsForShareBasedPaymentsAttributableToLtipUnits_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_AdjustmentsForShareBasedPaymentsAttributableToLtipUnits_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustments for share-based compensation to manager, LTIP Units to net cash flow from (used in) operating activities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_AdjustmentsForShareBasedPaymentsAttributableToLtipUnits_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustments for Share-based Payments Attributable to LTIP Units</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_AdjustmentsForShareBasedPaymentsAttributableToLtipUnits_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-based compensation to Manager - C-LTIP Units</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:to="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Operating Capital [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Changes in operating assets and liabilities:</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_IncreaseDecreaseDueFromToAffiliates" xlink:label="bhm_IncreaseDecreaseDueFromToAffiliates" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_IncreaseDecreaseDueFromToAffiliates" xlink:to="bhm_IncreaseDecreaseDueFromToAffiliates_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_IncreaseDecreaseDueFromToAffiliates_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The increase (decrease) during the reporting period in receivables to be collected from or obligations owed to an entity that is controlling, under the control of, or within the same control group as the reporting entity by means of direct or indirect ownership.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_IncreaseDecreaseDueFromToAffiliates_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) Due from to Affiliates</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="bhm_IncreaseDecreaseDueFromToAffiliates_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Due from affiliates, net</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_IncreaseDecreaseInAccountsReceivablePrepaidsAndOtherAssets" xlink:label="bhm_IncreaseDecreaseInAccountsReceivablePrepaidsAndOtherAssets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_IncreaseDecreaseInAccountsReceivablePrepaidsAndOtherAssets" xlink:to="bhm_IncreaseDecreaseInAccountsReceivablePrepaidsAndOtherAssets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_IncreaseDecreaseInAccountsReceivablePrepaidsAndOtherAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">It represents the increase (decrease) during the reporting period in the total amount of receivables from all parties and other operating assets not separately disclosed in the statement of cash flows.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_IncreaseDecreaseInAccountsReceivablePrepaidsAndOtherAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase Decrease In Accounts Receivable Prepaids and Other Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="bhm_IncreaseDecreaseInAccountsReceivablePrepaidsAndOtherAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts receivable, prepaids and other assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInNotesReceivableCurrent" xlink:label="us-gaap_IncreaseDecreaseInNotesReceivableCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInNotesReceivableCurrent" xlink:to="us-gaap_IncreaseDecreaseInNotesReceivableCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInNotesReceivableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Notes Receivable, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_IncreaseDecreaseInNotesReceivableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes and accrued interest receivable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInAccountsPayableAndOtherOperatingLiabilities" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayableAndOtherOperatingLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInAccountsPayableAndOtherOperatingLiabilities" xlink:to="us-gaap_IncreaseDecreaseInAccountsPayableAndOtherOperatingLiabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayableAndOtherOperatingLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Accounts Payable and Other Operating Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayableAndOtherOperatingLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts payable and other accrued liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Cash Provided by (Used in) Operating Activities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net cash (used in) provided by operating activities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:to="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Cash Provided by (Used in) Investing Activities [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash flows from investing activities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireRealEstateHeldForInvestment" xlink:label="us-gaap_PaymentsToAcquireRealEstateHeldForInvestment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsToAcquireRealEstateHeldForInvestment" xlink:to="us-gaap_PaymentsToAcquireRealEstateHeldForInvestment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsToAcquireRealEstateHeldForInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments to Acquire Real Estate Held-for-investment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_PaymentsToAcquireRealEstateHeldForInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquisitions of real estate investments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PaymentsToAcquireRealEstateHeldForInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquisitions of real estate investments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireProductiveAssets" xlink:label="us-gaap_PaymentsToAcquireProductiveAssets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsToAcquireProductiveAssets" xlink:to="us-gaap_PaymentsToAcquireProductiveAssets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsToAcquireProductiveAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments to Acquire Productive Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_PaymentsToAcquireProductiveAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capital expenditures</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromCollectionOfLongtermLoansToRelatedParties" xlink:label="us-gaap_ProceedsFromCollectionOfLongtermLoansToRelatedParties" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromCollectionOfLongtermLoansToRelatedParties" xlink:to="us-gaap_ProceedsFromCollectionOfLongtermLoansToRelatedParties_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromCollectionOfLongtermLoansToRelatedParties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Collection of Long-term Loans to Related Parties</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ProceedsFromCollectionOfLongtermLoansToRelatedParties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments on notes receivable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromSaleOfRealEstateHeldforinvestment" xlink:label="us-gaap_ProceedsFromSaleOfRealEstateHeldforinvestment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromSaleOfRealEstateHeldforinvestment" xlink:to="us-gaap_ProceedsFromSaleOfRealEstateHeldforinvestment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromSaleOfRealEstateHeldforinvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Sale of Real Estate Held-for-investment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ProceedsFromSaleOfRealEstateHeldforinvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from sale of real estate investments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:label="us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:to="us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments to Acquire Debt Securities, Available-for-Sale</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment in preferred equity investments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Original capital commitment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Cash Provided by (Used in) Investing Activities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net cash provided by investing activities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:to="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Cash Provided by (Used in) Financing Activities [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash flows from financing activities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfDividendsCommonStock" xlink:label="us-gaap_PaymentsOfDividendsCommonStock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsOfDividendsCommonStock" xlink:to="us-gaap_PaymentsOfDividendsCommonStock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsOfDividendsCommonStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments of Ordinary Dividends, Common Stock</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_PaymentsOfDividendsCommonStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Distributions to common stockholders</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfDividendsMinorityInterest" xlink:label="us-gaap_PaymentsOfDividendsMinorityInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsOfDividendsMinorityInterest" xlink:to="us-gaap_PaymentsOfDividendsMinorityInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsOfDividendsMinorityInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments of Ordinary Dividends, Noncontrolling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_PaymentsOfDividendsMinorityInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Distributions to noncontrolling interests</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_PaymentsOfDividendsToPartiallyOwnedNonControllingInterests" xlink:label="bhm_PaymentsOfDividendsToPartiallyOwnedNonControllingInterests" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_PaymentsOfDividendsToPartiallyOwnedNonControllingInterests" xlink:to="bhm_PaymentsOfDividendsToPartiallyOwnedNonControllingInterests_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_PaymentsOfDividendsToPartiallyOwnedNonControllingInterests_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of cash outflow in the form of ordinary dividends provided by the non-wholly owned subsidiary to partially owned noncontrolling interests.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_PaymentsOfDividendsToPartiallyOwnedNonControllingInterests_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments Of Dividends To Partially Owned Non Controlling Interests</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="bhm_PaymentsOfDividendsToPartiallyOwnedNonControllingInterests_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Distributions to partially owned properties' noncontrolling interests</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfDividendsPreferredStockAndPreferenceStock" xlink:label="us-gaap_PaymentsOfDividendsPreferredStockAndPreferenceStock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsOfDividendsPreferredStockAndPreferenceStock" xlink:to="us-gaap_PaymentsOfDividendsPreferredStockAndPreferenceStock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsOfDividendsPreferredStockAndPreferenceStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments of Ordinary Dividends, Preferred Stock and Preference Stock</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_PaymentsOfDividendsPreferredStockAndPreferenceStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Distributions to preferred stockholders</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_ProceedsFromPartiallyOwnedNoncontrollingInterests" xlink:label="bhm_ProceedsFromPartiallyOwnedNoncontrollingInterests" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_ProceedsFromPartiallyOwnedNoncontrollingInterests" xlink:to="bhm_ProceedsFromPartiallyOwnedNoncontrollingInterests_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_ProceedsFromPartiallyOwnedNoncontrollingInterests_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of cash inflow from partially owned noncontrolling interest. Includes, but is not limited to, purchase of additional shares or other increase in noncontrolling interest ownership.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_ProceedsFromPartiallyOwnedNoncontrollingInterests_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Partially Owned Noncontrolling Interests</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_ProceedsFromPartiallyOwnedNoncontrollingInterests_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contributions from noncontrolling interests</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RepaymentsOfNotesPayable" xlink:label="us-gaap_RepaymentsOfNotesPayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RepaymentsOfNotesPayable" xlink:to="us-gaap_RepaymentsOfNotesPayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RepaymentsOfNotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments of Notes Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_RepaymentsOfNotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments on mortgages payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RepaymentsOfLinesOfCredit" xlink:label="us-gaap_RepaymentsOfLinesOfCredit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RepaymentsOfLinesOfCredit" xlink:to="us-gaap_RepaymentsOfLinesOfCredit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RepaymentsOfLinesOfCredit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments of Lines of Credit</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_RepaymentsOfLinesOfCredit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments on revolving credit facilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfFinancingCosts" xlink:label="us-gaap_PaymentsOfFinancingCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsOfFinancingCosts" xlink:to="us-gaap_PaymentsOfFinancingCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsOfFinancingCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments of Financing Costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_PaymentsOfFinancingCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments of deferred financing fees</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromIssuanceOfRedeemablePreferredStock" xlink:label="us-gaap_ProceedsFromIssuanceOfRedeemablePreferredStock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromIssuanceOfRedeemablePreferredStock" xlink:to="us-gaap_ProceedsFromIssuanceOfRedeemablePreferredStock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromIssuanceOfRedeemablePreferredStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Issuance of Redeemable Preferred Stock</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromIssuanceOfRedeemablePreferredStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net proceeds from issuance of Redeemable Preferred Stock</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsForRepurchaseOfRedeemablePreferredStock" xlink:label="us-gaap_PaymentsForRepurchaseOfRedeemablePreferredStock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsForRepurchaseOfRedeemablePreferredStock" xlink:to="us-gaap_PaymentsForRepurchaseOfRedeemablePreferredStock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsForRepurchaseOfRedeemablePreferredStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments for Repurchase of Redeemable Preferred Stock</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_PaymentsForRepurchaseOfRedeemablePreferredStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments to redeem 6.0% Series A Redeemable Preferred Stock</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PaymentsForRepurchaseOfRedeemablePreferredStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Series A Preferred Stock redeemed, cash paid</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Cash Provided by (Used in) Financing Activities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net cash used in financing activities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash, Cash Equivalents, Restricted Cash and Restricted Cash Equivalents, Period Increase (Decrease), Including Exchange Rate Effect</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net (decrease) increase in cash, cash equivalents and restricted cash</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash, Cash Equivalents, Restricted Cash and Restricted Cash Equivalents</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash, cash equivalents and restricted cash, end of period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash, cash equivalents and restricted cash, beginning of year</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total cash, cash equivalents and restricted cash, end of period</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract" xlink:to="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash, Cash Equivalents, Restricted Cash and Restricted Cash Equivalents [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reconciliation of cash, cash equivalents and restricted cash</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SupplementalCashFlowInformationAbstract" xlink:label="us-gaap_SupplementalCashFlowInformationAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SupplementalCashFlowInformationAbstract" xlink:to="us-gaap_SupplementalCashFlowInformationAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SupplementalCashFlowInformationAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Supplemental Cash Flow Information [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_SupplementalCashFlowInformationAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Supplemental disclosure of cash flow information</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestPaidNet" xlink:label="us-gaap_InterestPaidNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestPaidNet" xlink:to="us-gaap_InterestPaidNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InterestPaidNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Paid, Excluding Capitalized Interest, Operating Activities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_InterestPaidNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash paid for interest (net of interest capitalized)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxesPaidNet" xlink:label="us-gaap_IncomeTaxesPaidNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeTaxesPaidNet" xlink:to="us-gaap_IncomeTaxesPaidNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeTaxesPaidNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income Taxes Paid, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeTaxesPaidNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash paid for income taxes</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:label="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:to="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash Flow, Noncash Investing and Financing Activities Disclosure [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Supplemental disclosure of non-cash investing and financing activities</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_AccrualOfDistributionsPayableToCommonUnitholders" xlink:label="bhm_AccrualOfDistributionsPayableToCommonUnitholders" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_AccrualOfDistributionsPayableToCommonUnitholders" xlink:to="bhm_AccrualOfDistributionsPayableToCommonUnitholders_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_AccrualOfDistributionsPayableToCommonUnitholders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrual of distributions payable to common unit holders during the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_AccrualOfDistributionsPayableToCommonUnitholders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrual Of Distributions Payable To Common Unitholders</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bhm_AccrualOfDistributionsPayableToCommonUnitholders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Distributions payable to common stockholders - declared and unpaid</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_AccrualOfDistributionsPayableToNonControllingInterestHolders" xlink:label="bhm_AccrualOfDistributionsPayableToNonControllingInterestHolders" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_AccrualOfDistributionsPayableToNonControllingInterestHolders" xlink:to="bhm_AccrualOfDistributionsPayableToNonControllingInterestHolders_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_AccrualOfDistributionsPayableToNonControllingInterestHolders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrual of distributions payable to non controlling interest holders during the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_AccrualOfDistributionsPayableToNonControllingInterestHolders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrual Of Distributions Payable To Non Controlling Interest Holders</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_AccrualOfDistributionsPayableToNonControllingInterestHolders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Distributions payable to noncontrolling interests - declared and unpaid</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_AccrualOfDistributionsPayableToPreferredUnitHolders" xlink:label="bhm_AccrualOfDistributionsPayableToPreferredUnitHolders" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_AccrualOfDistributionsPayableToPreferredUnitHolders" xlink:to="bhm_AccrualOfDistributionsPayableToPreferredUnitHolders_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_AccrualOfDistributionsPayableToPreferredUnitHolders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrual of distributions payable to preferred unit holders during the period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_AccrualOfDistributionsPayableToPreferredUnitHolders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrual Of Distributions Payable To Preferred Unit Holders</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_AccrualOfDistributionsPayableToPreferredUnitHolders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Distributions payable to preferred stockholders - declared and unpaid</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_CapitalExpendituresHeldInAccountsPayableAndOtherAccruedLiabilities" xlink:label="bhm_CapitalExpendituresHeldInAccountsPayableAndOtherAccruedLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_CapitalExpendituresHeldInAccountsPayableAndOtherAccruedLiabilities" xlink:to="bhm_CapitalExpendituresHeldInAccountsPayableAndOtherAccruedLiabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_CapitalExpendituresHeldInAccountsPayableAndOtherAccruedLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">This element represents the information regarding capital expenditures held in accounts payable and other accrued liabilities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_CapitalExpendituresHeldInAccountsPayableAndOtherAccruedLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capital Expenditures Held In Accounts Payable And Other Accrued Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_CapitalExpendituresHeldInAccountsPayableAndOtherAccruedLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capital expenditures held in accounts payable and other accrued liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:to="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Organization and Nature of Business</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NatureOfOperations" xlink:label="us-gaap_NatureOfOperations" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NatureOfOperations" xlink:to="us-gaap_NatureOfOperations_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NatureOfOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Nature of Operations [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_NatureOfOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Organization and Nature of Business</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountingPoliciesAbstract" xlink:label="us-gaap_AccountingPoliciesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountingPoliciesAbstract" xlink:to="us-gaap_AccountingPoliciesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountingPoliciesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Basis of Presentation and Summary of Significant Accounting Policies</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BasisOfPresentationAndSignificantAccountingPoliciesTextBlock" xlink:label="us-gaap_BasisOfPresentationAndSignificantAccountingPoliciesTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BasisOfPresentationAndSignificantAccountingPoliciesTextBlock" xlink:to="us-gaap_BasisOfPresentationAndSignificantAccountingPoliciesTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BasisOfPresentationAndSignificantAccountingPoliciesTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Basis of Presentation and Significant Accounting Policies [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_BasisOfPresentationAndSignificantAccountingPoliciesTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Basis of Presentation and Summary of Significant Accounting Policies</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationsAbstract" xlink:label="us-gaap_BusinessCombinationsAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationsAbstract" xlink:to="us-gaap_BusinessCombinationsAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquisition of Real Estate</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationDisclosureTextBlock" xlink:label="us-gaap_BusinessCombinationDisclosureTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationDisclosureTextBlock" xlink:to="us-gaap_BusinessCombinationDisclosureTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination Disclosure [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquisition of Real Estate</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_SaleOfRealEstateAssetsAbstract" xlink:label="bhm_SaleOfRealEstateAssetsAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_SaleOfRealEstateAssetsAbstract" xlink:to="bhm_SaleOfRealEstateAssetsAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_SaleOfRealEstateAssetsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">No definition available.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_SaleOfRealEstateAssetsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Real Estate Assets and Held for Sale Real Estate Assets</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_SaleOfRealEstateAssetsTextBlock" xlink:label="bhm_SaleOfRealEstateAssetsTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_SaleOfRealEstateAssetsTextBlock" xlink:to="bhm_SaleOfRealEstateAssetsTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_SaleOfRealEstateAssetsTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The disclosure of sale of real estate assets.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_SaleOfRealEstateAssetsTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Real Estate Assets [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_SaleOfRealEstateAssetsTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Real Estate Assets and Held for Sale Real Estate Assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateAbstract" xlink:label="us-gaap_RealEstateAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RealEstateAbstract" xlink:to="us-gaap_RealEstateAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RealEstateAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investments in Real Estate</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateDisclosureTextBlock" xlink:label="us-gaap_RealEstateDisclosureTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RealEstateDisclosureTextBlock" xlink:to="us-gaap_RealEstateDisclosureTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RealEstateDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Real Estate Disclosure [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RealEstateDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investments in Real Estate</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_NotesAndInterestReceivableDueFromRelatedPartiesAbstract" xlink:label="bhm_NotesAndInterestReceivableDueFromRelatedPartiesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_NotesAndInterestReceivableDueFromRelatedPartiesAbstract" xlink:to="bhm_NotesAndInterestReceivableDueFromRelatedPartiesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_NotesAndInterestReceivableDueFromRelatedPartiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">No definition available.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_NotesAndInterestReceivableDueFromRelatedPartiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes and Interest Receivable</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_NotesAndInterestReceivableDueFromRelatedPartyDisclosureTextBlock" xlink:label="bhm_NotesAndInterestReceivableDueFromRelatedPartyDisclosureTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_NotesAndInterestReceivableDueFromRelatedPartyDisclosureTextBlock" xlink:to="bhm_NotesAndInterestReceivableDueFromRelatedPartyDisclosureTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_NotesAndInterestReceivableDueFromRelatedPartyDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The entire disclosure for notes and interest receivable due from related party.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_NotesAndInterestReceivableDueFromRelatedPartyDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes And Interest Receivable Due From Related Party Disclosure [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bhm_NotesAndInterestReceivableDueFromRelatedPartyDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes and Interest Receivable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract" xlink:label="us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract" xlink:to="us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment in Unconsolidated Real Estate Fund</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_InvestmentInUnconsolidatedRealEstateFundUnderEquityMethodInvestmentTextBlock" xlink:label="bhm_InvestmentInUnconsolidatedRealEstateFundUnderEquityMethodInvestmentTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_InvestmentInUnconsolidatedRealEstateFundUnderEquityMethodInvestmentTextBlock" xlink:to="bhm_InvestmentInUnconsolidatedRealEstateFundUnderEquityMethodInvestmentTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_InvestmentInUnconsolidatedRealEstateFundUnderEquityMethodInvestmentTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The entire disclosure for investment in unconsolidated real estate fund under equity method investment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_InvestmentInUnconsolidatedRealEstateFundUnderEquityMethodInvestmentTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment In Unconsolidated Real Estate Fund Under Equity Method Investment [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_InvestmentInUnconsolidatedRealEstateFundUnderEquityMethodInvestmentTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment in Unconsolidated Real Estate Fund</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:label="us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:to="us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Equity Investments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock" xlink:label="us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock" xlink:to="us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investments in Debt and Marketable Equity Securities (and Certain Trading Assets) Disclosure [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Equity Investments</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_PrivatePlacementOfferingProgramAbstract" xlink:label="bhm_PrivatePlacementOfferingProgramAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_PrivatePlacementOfferingProgramAbstract" xlink:to="bhm_PrivatePlacementOfferingProgramAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_PrivatePlacementOfferingProgramAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">No definition available.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_PrivatePlacementOfferingProgramAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">DST Program</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_PrivatePlacementOfferingProgramTextBlock" xlink:label="bhm_PrivatePlacementOfferingProgramTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_PrivatePlacementOfferingProgramTextBlock" xlink:to="bhm_PrivatePlacementOfferingProgramTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_PrivatePlacementOfferingProgramTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The entire disclosure of information pertaining to the private placement offering program of the entity during the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_PrivatePlacementOfferingProgramTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Private Placement Offering Program [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_PrivatePlacementOfferingProgramTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">DST Program</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_RevolvingCreditFacilitiesAbstract" xlink:label="bhm_RevolvingCreditFacilitiesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_RevolvingCreditFacilitiesAbstract" xlink:to="bhm_RevolvingCreditFacilitiesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_RevolvingCreditFacilitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">No definition available.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_RevolvingCreditFacilitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revolving Credit Facilities</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_DisclosureOfRevolvingCreditFacilitiesTextBlock" xlink:label="bhm_DisclosureOfRevolvingCreditFacilitiesTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_DisclosureOfRevolvingCreditFacilitiesTextBlock" xlink:to="bhm_DisclosureOfRevolvingCreditFacilitiesTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityNoteAbstract" xlink:label="us-gaap_StockholdersEquityNoteAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:label="us-gaap_StockholdersEquityNoteDisclosureTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:to="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">New Accounting Pronouncements, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">New Accounting Pronouncements</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CreditLossFinancialInstrumentPolicyTextBlock" xlink:label="us-gaap_CreditLossFinancialInstrumentPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CreditLossFinancialInstrumentPolicyTextBlock" xlink:to="us-gaap_CreditLossFinancialInstrumentPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CreditLossFinancialInstrumentPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Credit Loss, Financial Instrument [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CreditLossFinancialInstrumentPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Current Expected Credit Losses</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_SignificantRisksAndUncertaintiesPolicyPolicyTextBlock" xlink:label="bhm_SignificantRisksAndUncertaintiesPolicyPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_SignificantRisksAndUncertaintiesPolicyPolicyTextBlock" xlink:to="bhm_SignificantRisksAndUncertaintiesPolicyPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_SignificantRisksAndUncertaintiesPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The disclosure of accounting policy for significant risks and uncertainties.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_SignificantRisksAndUncertaintiesPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Significant Risks And Uncertainties, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bhm_SignificantRisksAndUncertaintiesPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Significant Risks and Uncertainties</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_AccountingPoliciesTable" xlink:label="bhm_AccountingPoliciesTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_AccountingPoliciesTable" xlink:to="bhm_AccountingPoliciesTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_AccountingPoliciesTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounting Policies [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:label="us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:to="us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Assets by Major Class [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:label="us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:to="us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Assets, Major Class Name [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LeasesAcquiredInPlaceMember" xlink:label="us-gaap_LeasesAcquiredInPlaceMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LeasesAcquiredInPlaceMember" xlink:to="us-gaap_LeasesAcquiredInPlaceMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LeasesAcquiredInPlaceMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Leases, Acquired-in-Place [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LeasesAcquiredInPlaceMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">In-place lease intangible assets</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_RealEstateTaxAbatementMember" xlink:label="bhm_RealEstateTaxAbatementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_RealEstateTaxAbatementMember" xlink:to="bhm_RealEstateTaxAbatementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_RealEstateTaxAbatementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to real estate tax abatement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_RealEstateTaxAbatementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Real Estate Tax Abatement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_RealEstateTaxAbatementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Real estate tax abatement</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_AccountingPoliciesLineItems" xlink:label="bhm_AccountingPoliciesLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_AccountingPoliciesLineItems" xlink:to="bhm_AccountingPoliciesLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_AccountingPoliciesLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_AccountingPoliciesLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounting Policies [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_AccountingPoliciesLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Basis of Presentation and Summary of Significant Accounting Policies</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:label="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:to="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Finite-Lived Intangible Assets [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of intangible assets</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_ScheduleOfFiniteLivedIntangibleAssetActivityTableTextBlock" xlink:label="bhm_ScheduleOfFiniteLivedIntangibleAssetActivityTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_ScheduleOfFiniteLivedIntangibleAssetActivityTableTextBlock" xlink:to="bhm_ScheduleOfFiniteLivedIntangibleAssetActivityTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_ScheduleOfFiniteLivedIntangibleAssetActivityTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Tabular disclosure of changes during the period of assets, excluding financial assets and goodwill, lacking physical substance with a finite life, by either major class or business segment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_ScheduleOfFiniteLivedIntangibleAssetActivityTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule Of Finite Lived Intangible Asset Activity [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_ScheduleOfFiniteLivedIntangibleAssetActivityTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of in-place lease activity</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:label="us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:to="us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Finite-Lived Intangible Assets, Future Amortization Expense [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of estimated future amortization expense</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetAcquisitionTableTextBlock" xlink:label="us-gaap_AssetAcquisitionTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetAcquisitionTableTextBlock" xlink:to="us-gaap_AssetAcquisitionTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetAcquisitionTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetAcquisitionTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of the assets acquired at the acquisition date</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_RealEstateAssetsHeldForDevelopmentAndSaleTable" xlink:label="bhm_RealEstateAssetsHeldForDevelopmentAndSaleTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_RealEstateAssetsHeldForDevelopmentAndSaleTable" xlink:to="bhm_RealEstateAssetsHeldForDevelopmentAndSaleTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_RealEstateAssetsHeldForDevelopmentAndSaleTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disclosure of information about a  real estate properties .</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_RealEstateAssetsHeldForDevelopmentAndSaleTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Real Estate Assets Held for Development and Sale [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstatePropertiesAxis" xlink:label="us-gaap_RealEstatePropertiesAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RealEstatePropertiesAxis" xlink:to="us-gaap_RealEstatePropertiesAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RealEstatePropertiesAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Real Estate Property Ownership [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstatePropertiesDomain" xlink:label="us-gaap_RealEstatePropertiesDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RealEstatePropertiesDomain" xlink:to="us-gaap_RealEstatePropertiesDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RealEstatePropertiesDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Real Estate Properties [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConsolidatedPropertiesMember" xlink:label="us-gaap_ConsolidatedPropertiesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConsolidatedPropertiesMember" xlink:to="us-gaap_ConsolidatedPropertiesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConsolidatedPropertiesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consolidated operating investments [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConsolidatedPropertiesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consolidated investments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnconsolidatedPropertiesMember" xlink:label="us-gaap_UnconsolidatedPropertiesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_UnconsolidatedPropertiesMember" xlink:to="us-gaap_UnconsolidatedPropertiesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_UnconsolidatedPropertiesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unconsolidated Properties [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_UnconsolidatedPropertiesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred equity investments</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_RealEstateAssetsHeldForDevelopmentAndSaleLineItems" xlink:label="bhm_RealEstateAssetsHeldForDevelopmentAndSaleLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_RealEstateAssetsHeldForDevelopmentAndSaleLineItems" xlink:to="bhm_RealEstateAssetsHeldForDevelopmentAndSaleLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_RealEstateAssetsHeldForDevelopmentAndSaleLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line items represent financial concepts included in a tables. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the tables.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_RealEstateAssetsHeldForDevelopmentAndSaleLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Real Estate Assets Held for Development and Sale [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bhm_RealEstateAssetsHeldForDevelopmentAndSaleLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investments in Real Estate</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock" xlink:label="us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock" xlink:to="us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Real Estate Properties [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of the real estate investments</label>
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    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_ScheduleOfOfferingsInDelawareStatutoryTrustTableTextBlock" xlink:label="bhm_ScheduleOfOfferingsInDelawareStatutoryTrustTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfDebtInstrumentsTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Long-term Debt Instruments [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfDebtInstrumentsTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of senior mortgage indebtedness</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ContractualObligationFiscalYearMaturityScheduleTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of contractual principal payments of its borrowings</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:label="us-gaap_FairValueByBalanceSheetGroupingTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueByBalanceSheetGroupingTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of fair value of financial instruments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsMeasuredOnNonrecurringBasisTextBlock" xlink:label="us-gaap_FairValueAssetsMeasuredOnNonrecurringBasisTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueAssetsMeasuredOnNonrecurringBasisTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Measurements, Nonrecurring [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueAssetsMeasuredOnNonrecurringBasisTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of fair value of operating units classified as held for sale</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:label="us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:to="us-gaap_ScheduleOfDerivativeInstrumentsTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfDerivativeInstrumentsTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Derivative Instruments [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfDerivativeInstrumentsTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Derivative financial Instruments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock" xlink:label="us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfDerivativesInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of the fair value of the company's derivative financial instruments of balance sheets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDerivativeInstrumentsEffectOnOtherComprehensiveIncomeLossTableTextBlock" xlink:label="us-gaap_ScheduleOfDerivativeInstrumentsEffectOnOtherComprehensiveIncomeLossTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfDerivativeInstrumentsEffectOnOtherComprehensiveIncomeLossTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of the effect of derivative financial instruments on statements of operations and comprehensive income (loss)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TypeOfArrangementAxis" xlink:label="us-gaap_TypeOfArrangementAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ArrangementsAndNonarrangementTransactionsMember" xlink:label="us-gaap_ArrangementsAndNonarrangementTransactionsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_ManagementAgreementMember" xlink:label="bhm_ManagementAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_ManagementAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to management agreement.</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetManagementArrangementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Management Arrangement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetManagementArrangementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">DST Program</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_LeaseholdCostSharingAgreementMember" xlink:label="bhm_LeaseholdCostSharingAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_LeaseholdCostSharingAgreementMember" xlink:to="bhm_LeaseholdCostSharingAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_LeaseholdCostSharingAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to the Leasehold Cost-Sharing Agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_LeaseholdCostSharingAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Leasehold Cost Sharing Agreement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_LeaseholdCostSharingAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Leasehold Cost Sharing Agreement</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionLineItems" xlink:label="us-gaap_RelatedPartyTransactionLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_RelatedPartyTransactionLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyTransactionLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related Party Transaction [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_RelatedPartyTransactionLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related Party Transactions</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:to="us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Related Party Transactions [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of related party amounts payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfStockByClassTable" xlink:label="us-gaap_ScheduleOfStockByClassTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfStockByClassTable" xlink:to="us-gaap_ScheduleOfStockByClassTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfStockByClassTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Stock by Class [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfStockLineItems" xlink:label="us-gaap_ClassOfStockLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ClassOfStockLineItems" xlink:to="us-gaap_ClassOfStockLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ClassOfStockLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class of Stock [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ClassOfStockLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stockholders' Equity and Redeemable Preferred Stock</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ClassOfStockLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stockholders' Equity</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:to="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Earnings Per Share, Basic and Diluted [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of reconciliation of components of basic and diluted net (loss) income per common share</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_DistributionsOfDividendsDeclaredTableTextBlock" xlink:label="bhm_DistributionsOfDividendsDeclaredTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_DistributionsOfDividendsDeclaredTableTextBlock" xlink:to="bhm_DistributionsOfDividendsDeclaredTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_DistributionsOfDividendsDeclaredTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Tabular disclosure of information related to distributions of dividends declared.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_DistributionsOfDividendsDeclaredTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Distributions Of Dividends Declared [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_DistributionsOfDividendsDeclaredTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of dividends distributions to stock</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDividendsPayableTextBlock" xlink:label="us-gaap_ScheduleOfDividendsPayableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfDividendsPayableTextBlock" xlink:to="us-gaap_ScheduleOfDividendsPayableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfDividendsPayableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Dividends Payable [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfDividendsPayableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of distributions declared and paid</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, to be Paid, Maturity [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of future minimum lease payments and total operating lease liability</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTextBlock" xlink:label="us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTextBlock" xlink:to="us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reconciliation of Operating Profit (Loss) from Segments to Consolidated [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of NOI by reportable segments to consolidated</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:to="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Segment Reporting Information, by Segment [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of total rental and other property revenues for reportable segments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTable" xlink:label="us-gaap_SubsequentEventTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventTable" xlink:to="us-gaap_SubsequentEventTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent Event [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventLineItems" xlink:label="us-gaap_SubsequentEventLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventLineItems" xlink:to="us-gaap_SubsequentEventLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent Event [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SubsequentEventLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent Events</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DividendsDeclaredTableTextBlock" xlink:label="us-gaap_DividendsDeclaredTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DividendsDeclaredTableTextBlock" xlink:to="us-gaap_DividendsDeclaredTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DividendsDeclaredTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Dividends Declared [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DividendsDeclaredTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Declaration of Dividends</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_DistributionDeclaredAndOrPaidToStockholdersTableTextBlock" xlink:label="bhm_DistributionDeclaredAndOrPaidToStockholdersTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_DistributionDeclaredAndOrPaidToStockholdersTableTextBlock" xlink:to="bhm_DistributionDeclaredAndOrPaidToStockholdersTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_DistributionDeclaredAndOrPaidToStockholdersTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The tabular disclosure of distributions declared and/or paid to the Company's stockholders.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_DistributionDeclaredAndOrPaidToStockholdersTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Distribution Declared and/or Paid to Stockholders [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_DistributionDeclaredAndOrPaidToStockholdersTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of distributions declared and/or paid to the Company's stockholders</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRealEstatePropertiesTable" xlink:label="us-gaap_ScheduleOfRealEstatePropertiesTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfRealEstatePropertiesTable" xlink:to="us-gaap_ScheduleOfRealEstatePropertiesTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfRealEstatePropertiesTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Real Estate Properties [Table]</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_InvestmentsUnderDevelopmentMember" xlink:label="bhm_InvestmentsUnderDevelopmentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_InvestmentsUnderDevelopmentMember" xlink:to="bhm_InvestmentsUnderDevelopmentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_InvestmentsUnderDevelopmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Information pertaining to real estate properties and units within those properties that are under development.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_InvestmentsUnderDevelopmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investments Under Development [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_InvestmentsUnderDevelopmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investments under development</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstatePropertiesLineItems" xlink:label="us-gaap_RealEstatePropertiesLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RealEstatePropertiesLineItems" xlink:to="us-gaap_RealEstatePropertiesLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RealEstatePropertiesLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Real Estate Properties [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RealEstatePropertiesLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investments in Real Estate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_RealEstatePropertiesLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Real Estate Assets and Held for Sale Real Estate Assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfRealEstateProperties" xlink:label="us-gaap_NumberOfRealEstateProperties" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NumberOfRealEstateProperties" xlink:to="us-gaap_NumberOfRealEstateProperties_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NumberOfRealEstateProperties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of Real Estate Properties</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NumberOfRealEstateProperties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of real estate investments</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_NumberOfInvestments" xlink:label="bhm_NumberOfInvestments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_NumberOfInvestments" xlink:to="bhm_NumberOfInvestments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_NumberOfInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The number of investments.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_NumberOfInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of Investments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_NumberOfInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of investments</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_NumberOfInvestmentsThroughPreferredEquity" xlink:label="bhm_NumberOfInvestmentsThroughPreferredEquity" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_NumberOfInvestmentsThroughPreferredEquity" xlink:to="bhm_NumberOfInvestmentsThroughPreferredEquity_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_NumberOfInvestmentsThroughPreferredEquity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The number of investments through preferred equity.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_NumberOfInvestmentsThroughPreferredEquity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of Investments Through Preferred Equity</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_NumberOfInvestmentsThroughPreferredEquity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of investments through preferred equity</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_NumberOfUnconsolidatedRealEstateFundInvestment" xlink:label="bhm_NumberOfUnconsolidatedRealEstateFundInvestment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_NumberOfUnconsolidatedRealEstateFundInvestment" xlink:to="bhm_NumberOfUnconsolidatedRealEstateFundInvestment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_NumberOfUnconsolidatedRealEstateFundInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The number of unconsolidated real estate fund investment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_NumberOfUnconsolidatedRealEstateFundInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of Unconsolidated Real Estate Fund Investment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_NumberOfUnconsolidatedRealEstateFundInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of unconsolidated real estate fund investment</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_NumberOfConsolidatedAndPreferredEquityInvestments" xlink:label="bhm_NumberOfConsolidatedAndPreferredEquityInvestments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_NumberOfConsolidatedAndPreferredEquityInvestments" xlink:to="bhm_NumberOfConsolidatedAndPreferredEquityInvestments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_NumberOfConsolidatedAndPreferredEquityInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of consolidated and preferred equity investments.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_NumberOfConsolidatedAndPreferredEquityInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of Consolidated And Preferred Equity Investments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_NumberOfConsolidatedAndPreferredEquityInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of consolidated and preferred equity investments</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_NumberOfSingleFamilyResidentialHomes" xlink:label="bhm_NumberOfSingleFamilyResidentialHomes" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_NumberOfSingleFamilyResidentialHomes" xlink:to="bhm_NumberOfSingleFamilyResidentialHomes_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_NumberOfSingleFamilyResidentialHomes_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The number of single-family residential homes.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_NumberOfSingleFamilyResidentialHomes_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of Single-family Residential Homes</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_NumberOfSingleFamilyResidentialHomes_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of single-family residential homes</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_NumberOfInvestmentUnits" xlink:label="bhm_NumberOfInvestmentUnits" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_NumberOfInvestmentUnits" xlink:to="bhm_NumberOfInvestmentUnits_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_NumberOfInvestmentUnits_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The number of investment units</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_NumberOfInvestmentUnits_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of Investment Units</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_NumberOfInvestmentUnits_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of investment units</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_NumberOfConsolidatedUnitsUnderDevelopment" xlink:label="bhm_NumberOfConsolidatedUnitsUnderDevelopment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_NumberOfConsolidatedUnitsUnderDevelopment" xlink:to="bhm_NumberOfConsolidatedUnitsUnderDevelopment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_NumberOfConsolidatedUnitsUnderDevelopment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The number of consolidated units under development.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_NumberOfConsolidatedUnitsUnderDevelopment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of Consolidated Units Under Development</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_NumberOfConsolidatedUnitsUnderDevelopment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of investment units under development</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_NumberOfResidentialUnitsThroughPreferredEquityInvestments" xlink:label="bhm_NumberOfResidentialUnitsThroughPreferredEquityInvestments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_NumberOfResidentialUnitsThroughPreferredEquityInvestments" xlink:to="bhm_NumberOfResidentialUnitsThroughPreferredEquityInvestments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_NumberOfResidentialUnitsThroughPreferredEquityInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The number of residential units through preferred equity investments.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_NumberOfResidentialUnitsThroughPreferredEquityInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of Residential Units Through Preferred Equity Investments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_NumberOfResidentialUnitsThroughPreferredEquityInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of preferred equity investments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_OwnershipAxis" xlink:label="srt_OwnershipAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_OwnershipAxis" xlink:to="srt_OwnershipAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_OwnershipAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ownership [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_OwnershipDomain" xlink:label="srt_OwnershipDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_OwnershipDomain" xlink:to="srt_OwnershipDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_OwnershipDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ownership [Domain]</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_OpLtipUnitMember" xlink:label="bhm_OpLtipUnitMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_OpLtipUnitMember" xlink:to="bhm_OpLtipUnitMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_OpLtipUnitMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">This member stands for Op Ltip Unit.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_OpLtipUnitMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Op Ltip Unit [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_OpLtipUnitMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">OP LTIP Unit</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_OpUnitMember" xlink:label="bhm_OpUnitMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_OpUnitMember" xlink:to="bhm_OpUnitMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_OpUnitMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">This member stands for Op Unit.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_OpUnitMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Op Unit [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_OpUnitMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">OP Unit</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_LongtermIncentivePlanUnitsMember" xlink:label="bhm_LongtermIncentivePlanUnitsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_LongtermIncentivePlanUnitsMember" xlink:to="bhm_LongtermIncentivePlanUnitsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_LongtermIncentivePlanUnitsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">This member stands for long-term incentive plan.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_LongtermIncentivePlanUnitsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">LTIP Units [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_LongtermIncentivePlanUnitsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">LTIP Units</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPManagingMemberOrGeneralPartnerOwnershipInterest" xlink:label="us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPManagingMemberOrGeneralPartnerOwnershipInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPManagingMemberOrGeneralPartnerOwnershipInterest" xlink:to="us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPManagingMemberOrGeneralPartnerOwnershipInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPManagingMemberOrGeneralPartnerOwnershipInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Limited Liability Company (LLC) or Limited Partnership (LP), Managing Member or General Partner, Ownership Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPManagingMemberOrGeneralPartnerOwnershipInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Limited partners other than the company owned</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_PercentageOfUnvestedIncentivePlanInOperatingPartnership" xlink:label="bhm_PercentageOfUnvestedIncentivePlanInOperatingPartnership" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_PercentageOfUnvestedIncentivePlanInOperatingPartnership" xlink:to="bhm_PercentageOfUnvestedIncentivePlanInOperatingPartnership_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_PercentageOfUnvestedIncentivePlanInOperatingPartnership_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The percentage of unvested incentive plan in operating partnership.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_PercentageOfUnvestedIncentivePlanInOperatingPartnership_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage Of Unvested Incentive Plan In Operating Partnership</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_PercentageOfUnvestedIncentivePlanInOperatingPartnership_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of unvested incentive plan in operating partnership</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:label="us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:to="us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquired Finite-Lived Intangible Assets, Weighted Average Useful Life</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Estimated useful life</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AmortizationOfIntangibleAssets" xlink:label="us-gaap_AmortizationOfIntangibleAssets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AmortizationOfIntangibleAssets" xlink:to="us-gaap_AmortizationOfIntangibleAssets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AmortizationOfIntangibleAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amortization of Intangible Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_AmortizationOfIntangibleAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amortization</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AmortizationOfIntangibleAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amortization expense</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:label="us-gaap_FinitelivedIntangibleAssetsAcquired1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:to="us-gaap_FinitelivedIntangibleAssetsAcquired1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinitelivedIntangibleAssetsAcquired1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Assets Acquired</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinitelivedIntangibleAssetsAcquired1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquisitions</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_FinitelivedIntangibleAssetsAcquired1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchase price</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1" xlink:label="us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1" xlink:to="us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Assets, Remaining Amortization Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Estimated remaining useful life</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetImpairmentCharges" xlink:label="us-gaap_AssetImpairmentCharges" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetImpairmentCharges" xlink:to="us-gaap_AssetImpairmentCharges_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetImpairmentCharges_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Impairment Charges</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetImpairmentCharges_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset impairment charges</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_NumberOfRealEstateAssetsHeldForSale" xlink:label="bhm_NumberOfRealEstateAssetsHeldForSale" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_NumberOfRealEstateAssetsHeldForSale" xlink:to="bhm_NumberOfRealEstateAssetsHeldForSale_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_NumberOfRealEstateAssetsHeldForSale_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number classified as held for sale</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:label="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:to="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intangible Asset, Finite-Lived [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:label="us-gaap_FiniteLivedIntangibleAssetsLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:to="us-gaap_FiniteLivedIntangibleAssetsLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Assets [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Basis of Presentation and Summary of Significant Accounting Policies</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsGross" xlink:label="us-gaap_FiniteLivedIntangibleAssetsGross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsGross" xlink:to="us-gaap_FiniteLivedIntangibleAssetsGross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Assets, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gross carrying value</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:to="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Assets, Accumulated Amortization</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accumulated amortization</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsNet" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsNet" xlink:to="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Assets, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ending balance, December 31, 2024</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beginning balance, January 1, 2024</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net carrying value</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IndefiniteLivedIntangibleAssetsRollForward" xlink:label="us-gaap_IndefiniteLivedIntangibleAssetsRollForward" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IndefiniteLivedIntangibleAssetsRollForward" xlink:to="us-gaap_IndefiniteLivedIntangibleAssetsRollForward_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IndefiniteLivedIntangibleAssetsRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Indefinite-Lived Intangible Assets [Roll Forward]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IndefiniteLivedIntangibleAssetsRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intangible Assets</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_FiniteLivedIntangibleAssetExpectedAmortizationAfterYearOne" xlink:label="bhm_FiniteLivedIntangibleAssetExpectedAmortizationAfterYearOne" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_FiniteLivedIntangibleAssetExpectedAmortizationAfterYearOne" xlink:to="bhm_FiniteLivedIntangibleAssetExpectedAmortizationAfterYearOne_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_FiniteLivedIntangibleAssetExpectedAmortizationAfterYearOne_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of amortization for asset, excluding financial asset and goodwill, lacking physical substance with finite life expected to be recognized after first fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_FiniteLivedIntangibleAssetExpectedAmortizationAfterYearOne_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset, Expected Amortization, After Year One</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_FiniteLivedIntangibleAssetExpectedAmortizationAfterYearOne_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Expected amortization, after year one</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:to="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset, Expected Amortization, Remainder of Fiscal Year</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2026</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:to="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset, Expected Amortization, Year One</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:to="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset, Expected Amortization, Year Two</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2028</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:to="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset, Expected Amortization, Year Three</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2029</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:to="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset, Expected Amortization, Year Four</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2030</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFive" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFive" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFive" xlink:to="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFive_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFive_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset, Expected Amortization, after Year Five</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFive_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Thereafter</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:label="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:to="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Business Acquisitions, by Acquisition [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetAcquisitionAxis" xlink:label="us-gaap_AssetAcquisitionAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetAcquisitionAxis" xlink:to="us-gaap_AssetAcquisitionAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetAcquisitionAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetAcquisitionDomain" xlink:label="us-gaap_AssetAcquisitionDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetAcquisitionDomain" xlink:to="us-gaap_AssetAcquisitionDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetAcquisitionDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition [Domain]</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_ParksideAtSummersCornerMember" xlink:label="bhm_ParksideAtSummersCornerMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_ParksideAtSummersCornerMember" xlink:to="bhm_ParksideAtSummersCornerMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_ParksideAtSummersCornerMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to parkside at summers corner.</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_ParksideAtSummersCornerMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Parkside at Summers Corner</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionLineItems" xlink:label="us-gaap_BusinessAcquisitionLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionLineItems" xlink:to="us-gaap_BusinessAcquisitionLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessAcquisitionLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquisition of Real Estate</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_RealEstateNumberOfUnitsAcquired" xlink:label="bhm_RealEstateNumberOfUnitsAcquired" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_RealEstateNumberOfUnitsAcquired" xlink:to="bhm_RealEstateNumberOfUnitsAcquired_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_RealEstateNumberOfUnitsAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of units acquired under build to rent development projects at the end of the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_RealEstateNumberOfUnitsAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Real Estate, Number Of Units Acquired</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_RealEstateNumberOfUnitsAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of units acquired</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetAcquisitionConsiderationTransferred" xlink:label="us-gaap_AssetAcquisitionConsiderationTransferred" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetAcquisitionConsiderationTransferred" xlink:to="us-gaap_AssetAcquisitionConsiderationTransferred_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetAcquisitionConsiderationTransferred_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition, Consideration Transferred</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetAcquisitionConsiderationTransferred_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchase price, asset acquisition</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_RealEstateNumberOfUnitsCommittedToAcquire" xlink:label="bhm_RealEstateNumberOfUnitsCommittedToAcquire" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_RealEstateNumberOfUnitsCommittedToAcquire" xlink:to="bhm_RealEstateNumberOfUnitsCommittedToAcquire_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_RealEstateNumberOfUnitsCommittedToAcquire_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of units committed to acquired under build to rent development projects at the end of the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_RealEstateNumberOfUnitsCommittedToAcquire_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Real Estate, Number Of Units Committed To Acquire</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bhm_RealEstateNumberOfUnitsCommittedToAcquire_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of units committed to acquire</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetAcquisitionPriceOfAcquisitionExpected" xlink:label="us-gaap_AssetAcquisitionPriceOfAcquisitionExpected" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetAcquisitionPriceOfAcquisitionExpected" xlink:to="us-gaap_AssetAcquisitionPriceOfAcquisitionExpected_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetAcquisitionPriceOfAcquisitionExpected_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition, Price of Acquisition, Expected</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetAcquisitionPriceOfAcquisitionExpected_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">REPLACED WITH MORE ACCURATE ELEMENT Purchase price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AssetAcquisitionPriceOfAcquisitionExpected_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Aggregate purchase price</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetAcquisitionTable" xlink:label="us-gaap_AssetAcquisitionTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetAcquisitionTable" xlink:to="us-gaap_AssetAcquisitionTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetAcquisitionTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetAcquisitionLineItems" xlink:label="us-gaap_AssetAcquisitionLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetAcquisitionLineItems" xlink:to="us-gaap_AssetAcquisitionLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetAcquisitionLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetAcquisitionLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquisition of Real Estate</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_BuildingsGross" xlink:label="bhm_BuildingsGross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_BuildingsGross" xlink:to="bhm_BuildingsGross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_BuildingsGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount before accumulated depreciation of building structures held for productive use including addition, including, but not limited to, interior masonry, interior flooring, electrical, and plumbing.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_BuildingsGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Buildings, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_BuildingsGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Building</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_BuildingsImprovementsGross" xlink:label="bhm_BuildingsImprovementsGross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_BuildingsImprovementsGross" xlink:to="bhm_BuildingsImprovementsGross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_BuildingsImprovementsGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount before accumulated depreciation of building structures held for productive use improvement but not limited to, interior masonry, interior flooring, electrical, and plumbing.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_BuildingsImprovementsGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Buildings Improvements, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_BuildingsImprovementsGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Building improvements</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LandImprovements" xlink:label="us-gaap_LandImprovements" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LandImprovements" xlink:to="us-gaap_LandImprovements_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LandImprovements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Land Improvements</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LandImprovements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Land improvements</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_AssetAcquisitionCapitalizedExpenses" xlink:label="bhm_AssetAcquisitionCapitalizedExpenses" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_AssetAcquisitionCapitalizedExpenses" xlink:to="bhm_AssetAcquisitionCapitalizedExpenses_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_AssetAcquisitionCapitalizedExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of direct costs of the asset acquisition including legal, accounting, and other costs incurred to consummate the asset acquisition that have been capitalized.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_AssetAcquisitionCapitalizedExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition, Capitalized Expenses</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_AssetAcquisitionCapitalizedExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capitalized acquisition expenses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RealEstateAndAccumulatedDepreciationDescriptionOfPropertyAxis" xlink:label="srt_RealEstateAndAccumulatedDepreciationDescriptionOfPropertyAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RealEstateAndAccumulatedDepreciationDescriptionOfPropertyAxis" xlink:to="srt_RealEstateAndAccumulatedDepreciationDescriptionOfPropertyAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_RealEstateAndAccumulatedDepreciationDescriptionOfPropertyAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Name of Property [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RealEstateAndAccumulatedDepreciationNameOfPropertyDomain" xlink:label="srt_RealEstateAndAccumulatedDepreciationNameOfPropertyDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RealEstateAndAccumulatedDepreciationNameOfPropertyDomain" xlink:to="srt_RealEstateAndAccumulatedDepreciationNameOfPropertyDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_RealEstateAndAccumulatedDepreciationNameOfPropertyDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Name of Property [Domain]</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_IleMember" xlink:label="bhm_IleMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_IleMember" xlink:to="bhm_IleMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_IleMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to ILE.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_IleMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ile [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_IleMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ILE</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_IndySpringfieldPortfolioMember" xlink:label="bhm_IndySpringfieldPortfolioMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_IndySpringfieldPortfolioMember" xlink:to="bhm_IndySpringfieldPortfolioMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_IndySpringfieldPortfolioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information about Indy-Springfield portfolio.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_IndySpringfieldPortfolioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Indy Springfield Portfolio [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_IndySpringfieldPortfolioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Indy Springfield Portfolio</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_PeakJvTwoMember" xlink:label="bhm_PeakJvTwoMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_PeakJvTwoMember" xlink:to="bhm_PeakJvTwoMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_PeakJvTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to Peak JV 2 includes the portfolios formerly presented as Axelrod, Granbury, Granbury 2.0, Lubbock, Lubbock 2.0, Lubbock 3.0, Lynnwood, Lynnwood 2.0, Springtown, Springtown 2.0, Texarkana and Texas Portfolio 183, of which all are in Texas.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_PeakJvTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Peak JV Two [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_PeakJvTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Peak JV 2 portfolio</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bhm_PeakJvTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Peak JV 2</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_PeakJvThreeMember" xlink:label="bhm_PeakJvThreeMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_PeakJvThreeMember" xlink:to="bhm_PeakJvThreeMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_PeakJvThreeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to Peak JV 3 includes the portfolios formerly presented as DFW 189.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_PeakJvThreeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Peak JV Three [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_PeakJvThreeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Peak JV 3 portfolio</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bhm_PeakJvThreeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Peak JV 3</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_IleIndySpringfieldJv2PeakAndJv3PortfolioMember" xlink:label="bhm_IleIndySpringfieldJv2PeakAndJv3PortfolioMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_IleIndySpringfieldJv2PeakAndJv3PortfolioMember" xlink:to="bhm_IleIndySpringfieldJv2PeakAndJv3PortfolioMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_IleIndySpringfieldJv2PeakAndJv3PortfolioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to ILE, Indy-Springfield, Jv2 Peak and Jv3 Portfolio.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_IleIndySpringfieldJv2PeakAndJv3PortfolioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ILE,Indy-Springfield, Jv2 Peak and Jv3 Portfolio [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_IleIndySpringfieldJv2PeakAndJv3PortfolioMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ILE, Indy-Springfield, Peak JV2 and JV3 Portfolio</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_BallastMember" xlink:label="bhm_BallastMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_BallastMember" xlink:to="bhm_BallastMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_BallastMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to the Ballast</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_BallastMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ballast [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_BallastMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ballast</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_GoldenPacificMember" xlink:label="bhm_GoldenPacificMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_GoldenPacificMember" xlink:to="bhm_GoldenPacificMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_GoldenPacificMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">This member stands for golden pacific.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_GoldenPacificMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Golden Pacific [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_GoldenPacificMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Golden Pacific</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_NumberOfUnitsSoldInRealEstateProperty" xlink:label="bhm_NumberOfUnitsSoldInRealEstateProperty" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_NumberOfUnitsSoldInRealEstateProperty" xlink:to="bhm_NumberOfUnitsSoldInRealEstateProperty_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_NumberOfUnitsSoldInRealEstateProperty_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of units sold in real estate properties.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_NumberOfUnitsSoldInRealEstateProperty_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of Units Sold in Real Estate Property</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_NumberOfUnitsSoldInRealEstateProperty_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of units sold in real estate properties</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_ProceedsFromSaleOfRealEstateGross" xlink:label="bhm_ProceedsFromSaleOfRealEstateGross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_ProceedsFromSaleOfRealEstateGross" xlink:to="bhm_ProceedsFromSaleOfRealEstateGross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_ProceedsFromSaleOfRealEstateGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of sale of real estate properties.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_ProceedsFromSaleOfRealEstateGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds From Sale Of Real Estate Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bhm_ProceedsFromSaleOfRealEstateGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Aggregate sale of real estate transactions</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_NumberOfUnitsEncumberedInRealEstateProperty" xlink:label="bhm_NumberOfUnitsEncumberedInRealEstateProperty" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_NumberOfUnitsEncumberedInRealEstateProperty" xlink:to="bhm_NumberOfUnitsEncumberedInRealEstateProperty_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_NumberOfUnitsEncumberedInRealEstateProperty_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of units encumbered in real estate property.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_NumberOfUnitsEncumberedInRealEstateProperty_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of Units Encumbered in Real Estate Property</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_NumberOfUnitsEncumberedInRealEstateProperty_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of units encumbered</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MortgageLoanRelatedToPropertySales1" xlink:label="us-gaap_MortgageLoanRelatedToPropertySales1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MortgageLoanRelatedToPropertySales1" xlink:to="us-gaap_MortgageLoanRelatedToPropertySales1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MortgageLoanRelatedToPropertySales1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Mortgage Loan Related to Property Sales</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MortgageLoanRelatedToPropertySales1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Mortgage loan related to property sales</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromSaleOfRealEstate" xlink:label="us-gaap_ProceedsFromSaleOfRealEstate" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromSaleOfRealEstate" xlink:to="us-gaap_ProceedsFromSaleOfRealEstate_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromSaleOfRealEstate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Sale of Real Estate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromSaleOfRealEstate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net proceeds from sale of units in real estate</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainOnSaleOfInvestments" xlink:label="us-gaap_GainOnSaleOfInvestments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GainOnSaleOfInvestments" xlink:to="us-gaap_GainOnSaleOfInvestments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GainOnSaleOfInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain on Sale of Investments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GainOnSaleOfInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain on sale of real estate investments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:label="srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:to="srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Real Estate, Type of Property [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MortgageLoansOnRealEstateNamePropertyTypeDomain" xlink:label="srt_MortgageLoansOnRealEstateNamePropertyTypeDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_MortgageLoansOnRealEstateNamePropertyTypeDomain" xlink:to="srt_MortgageLoansOnRealEstateNamePropertyTypeDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_MortgageLoansOnRealEstateNamePropertyTypeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Real Estate [Domain]</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_RealEstatePropertyHeldForSaleMember" xlink:label="bhm_RealEstatePropertyHeldForSaleMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_RealEstatePropertyHeldForSaleMember" xlink:to="bhm_RealEstatePropertyHeldForSaleMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_RealEstatePropertyHeldForSaleMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to Real Estate Held For Sale.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_RealEstatePropertyHeldForSaleMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Real Estate Property Held For Sale [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_RealEstatePropertyHeldForSaleMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Real Estate Property Held For Sale</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_AllureAtSouthparkMember" xlink:label="bhm_AllureAtSouthparkMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_AllureAtSouthparkMember" xlink:to="bhm_AllureAtSouthparkMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_AllureAtSouthparkMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Allure at Southpark.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_AllureAtSouthparkMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Allure at Southpark [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_AllureAtSouthparkMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Allure at Southpark</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_AmiraAtWestlyMember" xlink:label="bhm_AmiraAtWestlyMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_AmiraAtWestlyMember" xlink:to="bhm_AmiraAtWestlyMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_AmiraAtWestlyMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information about Amira at Westly.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_AmiraAtWestlyMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amira at Westly [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_AmiraAtWestlyMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amira at Westly</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_AvenueAtTimberlinParkMember" xlink:label="bhm_AvenueAtTimberlinParkMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_AvenueAtTimberlinParkMember" xlink:to="bhm_AvenueAtTimberlinParkMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_AvenueAtTimberlinParkMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the Avenue at Timberlin Park.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_AvenueAtTimberlinParkMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Avenue at Timberlin Park [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_AvenueAtTimberlinParkMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Avenue at Timberlin Park</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_DistrictAtParkviewMember" xlink:label="bhm_DistrictAtParkviewMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_DistrictAtParkviewMember" xlink:to="bhm_DistrictAtParkviewMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_DistrictAtParkviewMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to district at parkview.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_DistrictAtParkviewMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">District At Parkview [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_DistrictAtParkviewMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">District at Parkview</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_SkytopApartmentsMember" xlink:label="bhm_SkytopApartmentsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_SkytopApartmentsMember" xlink:to="bhm_SkytopApartmentsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_SkytopApartmentsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to skytop apartments.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_SkytopApartmentsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Skytop Apartments [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_SkytopApartmentsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Skytop Apartments</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_SouthernPinesReserveMember" xlink:label="bhm_SouthernPinesReserveMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_SouthernPinesReserveMember" xlink:to="bhm_SouthernPinesReserveMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_SouthernPinesReserveMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Southern Pines Reserve.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_SouthernPinesReserveMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Southern Pines Reserve [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_SouthernPinesReserveMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Southern Pines Reserve</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_VillasAtHuffmeisterMember" xlink:label="bhm_VillasAtHuffmeisterMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_VillasAtHuffmeisterMember" xlink:to="bhm_VillasAtHuffmeisterMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_VillasAtHuffmeisterMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information about Villas at Huffmeister.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_VillasAtHuffmeisterMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Villas at Huffmeister [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_VillasAtHuffmeisterMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Villas at Huffmeister</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_WayfordAtConcordMember" xlink:label="bhm_WayfordAtConcordMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_WayfordAtConcordMember" xlink:to="bhm_WayfordAtConcordMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_WayfordAtConcordMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to Wayford at Concord.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_WayfordAtConcordMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Wayford At Concord [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_WayfordAtConcordMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Wayford at Concord</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_YaugerParkVillasMember" xlink:label="bhm_YaugerParkVillasMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_YaugerParkVillasMember" xlink:to="bhm_YaugerParkVillasMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_YaugerParkVillasMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to Yauger Park Villas.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_YaugerParkVillasMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Yauger Park Villas [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_YaugerParkVillasMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Yauger Park Villas</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_IndySpringfieldMember" xlink:label="bhm_IndySpringfieldMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_IndySpringfieldMember" xlink:to="bhm_IndySpringfieldMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_IndySpringfieldMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to Indy-Springfield, formerly Peak JV I.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_IndySpringfieldMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Indy-Springfield [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_IndySpringfieldMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Indy-Springfield</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_Savannah84Member" xlink:label="bhm_Savannah84Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_Savannah84Member" xlink:to="bhm_Savannah84Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_Savannah84Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to Savannah-84,  formerly Peak JV IV.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_Savannah84Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Savannah-84 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_Savannah84Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Savannah-84</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_AbodeWendellFallsMember" xlink:label="bhm_AbodeWendellFallsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_AbodeWendellFallsMember" xlink:to="bhm_AbodeWendellFallsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_AbodeWendellFallsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to Abode Wendell Falls.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_AbodeWendellFallsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Abode Wendell Falls [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_AbodeWendellFallsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Abode Wendell Falls</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_HarmonyAtClearCreekMember" xlink:label="bhm_HarmonyAtClearCreekMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_HarmonyAtClearCreekMember" xlink:to="bhm_HarmonyAtClearCreekMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_HarmonyAtClearCreekMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Harmony at clear creek.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_HarmonyAtClearCreekMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Harmony At Clear Creek [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_HarmonyAtClearCreekMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Harmony at Clear Creek</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementBusinessSegmentsAxis" xlink:label="us-gaap_StatementBusinessSegmentsAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementBusinessSegmentsAxis" xlink:to="us-gaap_StatementBusinessSegmentsAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementBusinessSegmentsAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Segments [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentDomain" xlink:label="us-gaap_SegmentDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentDomain" xlink:to="us-gaap_SegmentDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SegmentDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Segments [Domain]</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_ResidentialCommunitiesSegmentMember" xlink:label="bhm_ResidentialCommunitiesSegmentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_ResidentialCommunitiesSegmentMember" xlink:to="bhm_ResidentialCommunitiesSegmentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_ResidentialCommunitiesSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information relating to Residential communities segment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_ResidentialCommunitiesSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Residential Communities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_ResidentialCommunitiesSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Residential communities</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_ScatteredSingleFamilyHomesSegmentMember" xlink:label="bhm_ScatteredSingleFamilyHomesSegmentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_ScatteredSingleFamilyHomesSegmentMember" xlink:to="bhm_ScatteredSingleFamilyHomesSegmentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_ScatteredSingleFamilyHomesSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information relating to Scattered single-family homes segment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_ScatteredSingleFamilyHomesSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Scattered Single-Family Homes</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_ScatteredSingleFamilyHomesSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Scattered single-family homes</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_InvestmentsInOperatingStatusMember" xlink:label="bhm_InvestmentsInOperatingStatusMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_InvestmentsInOperatingStatusMember" xlink:to="bhm_InvestmentsInOperatingStatusMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_InvestmentsInOperatingStatusMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Information pertaining to real estate properties and units within those properties that are in operating status.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_InvestmentsInOperatingStatusMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investments In Operating Status [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_InvestmentsInOperatingStatusMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating investments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RealEstateAndAccumulatedDepreciationLineItems" xlink:label="srt_RealEstateAndAccumulatedDepreciationLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RealEstateAndAccumulatedDepreciationLineItems" xlink:to="srt_RealEstateAndAccumulatedDepreciationLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_RealEstateAndAccumulatedDepreciationLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SEC Schedule, 12-28, Real Estate Companies, Investment in Real Estate and Accumulated Depreciation [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_RealEstateAndAccumulatedDepreciationLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investments in Real Estate</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_RealEstatePropertyLocation" xlink:label="bhm_RealEstatePropertyLocation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_RealEstatePropertyLocation" xlink:to="bhm_RealEstatePropertyLocation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_RealEstatePropertyLocation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">It represents the real estate property location.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_RealEstatePropertyLocation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Real Estate Property Location</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_RealEstatePropertyLocation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Location / Market</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bhm_RealEstatePropertyLocation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Location</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_OwnershipPercentageOnInvestments" xlink:label="bhm_OwnershipPercentageOnInvestments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_OwnershipPercentageOnInvestments" xlink:to="bhm_OwnershipPercentageOnInvestments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_OwnershipPercentageOnInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The percentage of ownership interest on investments.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_OwnershipPercentageOnInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ownership Percentage on Investments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_OwnershipPercentageOnInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ownership Interest (as a percent)</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_RealEstateNumberOfUnitsDelivered" xlink:label="bhm_RealEstateNumberOfUnitsDelivered" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_RealEstateNumberOfUnitsDelivered" xlink:to="bhm_RealEstateNumberOfUnitsDelivered_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_RealEstateNumberOfUnitsDelivered_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of units delivered under the build to rent development projects at the end of the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_RealEstateNumberOfUnitsDelivered_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Real Estate, Number Of Units Delivered</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_RealEstateNumberOfUnitsDelivered_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of units delivered</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_NumberOfOperatingInvestmentUnits" xlink:label="bhm_NumberOfOperatingInvestmentUnits" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_NumberOfOperatingInvestmentUnits" xlink:to="bhm_NumberOfOperatingInvestmentUnits_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_NumberOfOperatingInvestmentUnits_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The number of operating investment units</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_NumberOfOperatingInvestmentUnits_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of Operating Investment Units</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bhm_NumberOfOperatingInvestmentUnits_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total development units</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Depreciation" xlink:label="us-gaap_Depreciation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Depreciation" xlink:to="us-gaap_Depreciation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Depreciation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Depreciation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_Depreciation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Depreciation expense, Investments in real estate</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_UnconsolidatedPropertiesInDevelopmentStatusMember" xlink:label="bhm_UnconsolidatedPropertiesInDevelopmentStatusMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_UnconsolidatedPropertiesInDevelopmentStatusMember" xlink:to="bhm_UnconsolidatedPropertiesInDevelopmentStatusMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_UnconsolidatedPropertiesInDevelopmentStatusMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Information pertaining to real estate properties and units within those properties that are partially owned that are not consolidated within the entity's financial statements and which are in development status.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_UnconsolidatedPropertiesInDevelopmentStatusMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unconsolidated Properties In Development Status [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_UnconsolidatedPropertiesInDevelopmentStatusMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred equity - Development</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_UnconsolidatedPropertiesInOperatingStatusMember" xlink:label="bhm_UnconsolidatedPropertiesInOperatingStatusMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_UnconsolidatedPropertiesInOperatingStatusMember" xlink:to="bhm_UnconsolidatedPropertiesInOperatingStatusMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_UnconsolidatedPropertiesInOperatingStatusMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Information pertaining to real estate properties and units within those properties that are partially owned that are not consolidated within the entity's financial statements and which are in operating status.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_UnconsolidatedPropertiesInOperatingStatusMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unconsolidated Properties In Operating Status [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_UnconsolidatedPropertiesInOperatingStatusMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred equity - Operating</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_ArcherAtRiverblueMember" xlink:label="bhm_ArcherAtRiverblueMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_ArcherAtRiverblueMember" xlink:to="bhm_ArcherAtRiverblueMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_ArcherAtRiverblueMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Archer at RiverBlue.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_ArcherAtRiverblueMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Archer At RiverBlue [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_ArcherAtRiverblueMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Archer at RiverBlue</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_CanvasAtWildwoodMember" xlink:label="bhm_CanvasAtWildwoodMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_CanvasAtWildwoodMember" xlink:to="bhm_CanvasAtWildwoodMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_CanvasAtWildwoodMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Canvas at Wildwood.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_CanvasAtWildwoodMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Canvas at Wildwood</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_CanvasAtWildwoodMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Canvas at Wildwood</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_RiverFordMember" xlink:label="bhm_RiverFordMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_RiverFordMember" xlink:to="bhm_RiverFordMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_RiverFordMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to River Ford.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_RiverFordMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">River Ford</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_RiverFordMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">River Ford</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_SanfordMarketplaceMember" xlink:label="bhm_SanfordMarketplaceMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_SanfordMarketplaceMember" xlink:to="bhm_SanfordMarketplaceMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_SanfordMarketplaceMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Sanford Marketplace.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_SanfordMarketplaceMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sanford Marketplace [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_SanfordMarketplaceMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sanford Marketplace</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_WayfordAtInnovationParkMember" xlink:label="bhm_WayfordAtInnovationParkMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_WayfordAtInnovationParkMember" xlink:to="bhm_WayfordAtInnovationParkMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_WayfordAtInnovationParkMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to Wayford at Innovation Park.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_WayfordAtInnovationParkMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Wayford at Innovation Park [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_WayfordAtInnovationParkMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Wayford at Innovation Park</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfUnitsInRealEstateProperty" xlink:label="us-gaap_NumberOfUnitsInRealEstateProperty" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NumberOfUnitsInRealEstateProperty" xlink:to="us-gaap_NumberOfUnitsInRealEstateProperty_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NumberOfUnitsInRealEstateProperty_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of Units in Real Estate Property</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_NumberOfUnitsInRealEstateProperty_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of units</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xlink:label="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xlink:to="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Accounts, Notes, Loans and Financing Receivable [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsNotesAndLoansReceivableLineItems" xlink:label="us-gaap_AccountsNotesAndLoansReceivableLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsNotesAndLoansReceivableLineItems" xlink:to="us-gaap_AccountsNotesAndLoansReceivableLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsNotesAndLoansReceivableLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts, Notes, Loans and Financing Receivable [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AccountsNotesAndLoansReceivableLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes and Interest Receivables</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAndFee" xlink:label="us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAndFee" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAndFee" xlink:to="us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAndFee_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAndFee_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Receivable, before Allowance for Credit Loss, Fee and Loan in Process</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAndFee_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loan investments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableAccruedInterestBeforeAllowanceForCreditLoss" xlink:label="us-gaap_FinancingReceivableAccruedInterestBeforeAllowanceForCreditLoss" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinancingReceivableAccruedInterestBeforeAllowanceForCreditLoss" xlink:to="us-gaap_FinancingReceivableAccruedInterestBeforeAllowanceForCreditLoss_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinancingReceivableAccruedInterestBeforeAllowanceForCreditLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Receivable, Accrued Interest, before Allowance for Credit Loss</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_FinancingReceivableAccruedInterestBeforeAllowanceForCreditLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Outstanding interest receivable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableAllowanceForCreditLosses" xlink:label="us-gaap_FinancingReceivableAllowanceForCreditLosses" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinancingReceivableAllowanceForCreditLosses" xlink:to="us-gaap_FinancingReceivableAllowanceForCreditLosses_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinancingReceivableAllowanceForCreditLosses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Receivable, Allowance for Credit Loss</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_FinancingReceivableAllowanceForCreditLosses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Allowance for credit losses, net, end of period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_FinancingReceivableAllowanceForCreditLosses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beginning balance, net as of January 1, 2025</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinancingReceivableAllowanceForCreditLosses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Allowance for credit losses</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_FinancingReceivableAllowanceForCreditLossPoolOfAssets" xlink:label="bhm_FinancingReceivableAllowanceForCreditLossPoolOfAssets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_FinancingReceivableAllowanceForCreditLossPoolOfAssets" xlink:to="bhm_FinancingReceivableAllowanceForCreditLossPoolOfAssets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_FinancingReceivableAllowanceForCreditLossPoolOfAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of Financing Receivable, Allowance for Credit Loss, Pool of assets.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_FinancingReceivableAllowanceForCreditLossPoolOfAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Financing Receivable, Allowance for Credit Loss, Pool of Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_FinancingReceivableAllowanceForCreditLossPoolOfAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Recovery of credit losses on pool of assets, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:label="srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:to="srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment, Name [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_EquityMethodInvesteeNameDomain" xlink:label="srt_EquityMethodInvesteeNameDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_EquityMethodInvesteeNameDomain" xlink:to="srt_EquityMethodInvesteeNameDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_EquityMethodInvesteeNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment, Name [Domain]</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_WayfordAtPringleMember" xlink:label="bhm_WayfordAtPringleMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_WayfordAtPringleMember" xlink:to="bhm_WayfordAtPringleMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_WayfordAtPringleMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information about Wayford at Pringle.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_WayfordAtPringleMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Wayford at Pringle [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_WayfordAtPringleMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Wayford at Pringle</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_WillowParkMember" xlink:label="bhm_WillowParkMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_WillowParkMember" xlink:to="bhm_WillowParkMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_WillowParkMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to Willow Park.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_WillowParkMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Willow Park [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bhm_WillowParkMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Willow Park</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:to="us-gaap_ScheduleOfEquityMethodInvestmentsTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Equity Method Investments [Table]</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_MarbleCapitalIncomeAndImpactFundLpMember" xlink:label="bhm_MarbleCapitalIncomeAndImpactFundLpMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_MarbleCapitalIncomeAndImpactFundLpMember" xlink:to="bhm_MarbleCapitalIncomeAndImpactFundLpMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_MarbleCapitalIncomeAndImpactFundLpMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Interest in Marble Capital Income and Impact Fund, LP.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_MarbleCapitalIncomeAndImpactFundLpMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Marble Capital Income and Impact Fund, LP [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_MarbleCapitalIncomeAndImpactFundLpMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Marble Capital Income and Impact Fund, LP</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:to="us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Equity Method Investments [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment in Unconsolidated Real Estate Fund</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Equity Investments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:label="us-gaap_EquityMethodInvestmentOwnershipPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:to="us-gaap_EquityMethodInvestmentOwnershipPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityMethodInvestmentOwnershipPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment, Ownership Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EquityMethodInvestmentOwnershipPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ownership interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis" xlink:label="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis" xlink:to="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment, Nonconsolidated Investee [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain" xlink:label="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain" xlink:to="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment, Nonconsolidated Investee [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Investments" xlink:label="us-gaap_Investments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Investments" xlink:to="us-gaap_Investments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Investments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_Investments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investments</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_ReceivableAndOtherAssets" xlink:label="bhm_ReceivableAndOtherAssets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_ReceivableAndOtherAssets" xlink:to="bhm_ReceivableAndOtherAssets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_ReceivableAndOtherAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of receivable and assets classified as other.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_ReceivableAndOtherAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Receivable And Other Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_ReceivableAndOtherAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Receivables and other assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PartnersCapital" xlink:label="us-gaap_PartnersCapital" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PartnersCapital" xlink:to="us-gaap_PartnersCapital_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PartnersCapital_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Partners' Capital</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PartnersCapital_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Partners' capital</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MembersEquityAttributableToNoncontrollingInterest" xlink:label="us-gaap_MembersEquityAttributableToNoncontrollingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MembersEquityAttributableToNoncontrollingInterest" xlink:to="us-gaap_MembersEquityAttributableToNoncontrollingInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MembersEquityAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Members' Equity Attributable to Noncontrolling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MembersEquityAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-controlling interest</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_InterestIncomeOnInvestment" xlink:label="bhm_InterestIncomeOnInvestment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_InterestIncomeOnInvestment" xlink:to="bhm_InterestIncomeOnInvestment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_InterestIncomeOnInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">It represents the amount of interest income relates to investment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_InterestIncomeOnInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Income On Investment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_InterestIncomeOnInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment income</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentIncomeInvestmentExpense" xlink:label="us-gaap_InvestmentIncomeInvestmentExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentIncomeInvestmentExpense" xlink:to="us-gaap_InvestmentIncomeInvestmentExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InvestmentIncomeInvestmentExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment Income, Investment Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_InvestmentIncomeInvestmentExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Expenses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentIncomeNet" xlink:label="us-gaap_InvestmentIncomeNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentIncomeNet" xlink:to="us-gaap_InvestmentIncomeNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InvestmentIncomeNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment Income, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_InvestmentIncomeNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net investment income</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnInvestments" xlink:label="us-gaap_GainLossOnInvestments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GainLossOnInvestments" xlink:to="us-gaap_GainLossOnInvestments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GainLossOnInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (Loss) on Investments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GainLossOnInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net unrealized gain on investments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PartnersCapitalAccountPeriodIncreaseDecrease" xlink:label="us-gaap_PartnersCapitalAccountPeriodIncreaseDecrease" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PartnersCapitalAccountPeriodIncreaseDecrease" xlink:to="us-gaap_PartnersCapitalAccountPeriodIncreaseDecrease_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PartnersCapitalAccountPeriodIncreaseDecrease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Partners' Capital</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:label="us-gaap_PartnersCapitalAccountPeriodIncreaseDecrease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net increase in partners' capital</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_PreferredEquityJointVentureAgreementsCount" xlink:label="bhm_PreferredEquityJointVentureAgreementsCount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_PreferredEquityJointVentureAgreementsCount" xlink:to="bhm_PreferredEquityJointVentureAgreementsCount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_PreferredEquityJointVentureAgreementsCount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of joint venture agreements entered into for preferred equity investments classified as available-for-sale debt securities as of the reporting date.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_PreferredEquityJointVentureAgreementsCount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Equity Joint Venture Agreements Count</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_PreferredEquityJointVentureAgreementsCount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of joint venture agreements for preferred equity investments</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_InvestmentIncomeDebtSecuritiesAvailableForSaleNonOperating" xlink:label="bhm_InvestmentIncomeDebtSecuritiesAvailableForSaleNonOperating" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_InvestmentIncomeDebtSecuritiesAvailableForSaleNonOperating" xlink:to="bhm_InvestmentIncomeDebtSecuritiesAvailableForSaleNonOperating_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_InvestmentIncomeDebtSecuritiesAvailableForSaleNonOperating_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of investment income, amortization of premium and accretion of discount on investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale); classified as non-operating.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_InvestmentIncomeDebtSecuritiesAvailableForSaleNonOperating_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment Income, Debt Securities, Available for Sale, Non-Operating</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_InvestmentIncomeDebtSecuritiesAvailableForSaleNonOperating_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleAccumulatedGrossUnrealizedGainLossBeforeTax" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAccumulatedGrossUnrealizedGainLossBeforeTax" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtSecuritiesAvailableForSaleAccumulatedGrossUnrealizedGainLossBeforeTax" xlink:to="us-gaap_DebtSecuritiesAvailableForSaleAccumulatedGrossUnrealizedGainLossBeforeTax_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAccumulatedGrossUnrealizedGainLossBeforeTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Securities, Available-for-Sale, Accumulated Gross Unrealized Gain (Loss), before Tax</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAccumulatedGrossUnrealizedGainLossBeforeTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gross unrealized gain, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Securities, Available-for-Sale, Maturity, Allocated and Single Maturity Date, Amortized Cost [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasisAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net carrying amount</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated and Single Maturity Date, Year One</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Due within one year</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_DebtSecuritiesAvailableForSaleAmortizedCostMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughThree" xlink:label="bhm_DebtSecuritiesAvailableForSaleAmortizedCostMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughThree" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_DebtSecuritiesAvailableForSaleAmortizedCostMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughThree" xlink:to="bhm_DebtSecuritiesAvailableForSaleAmortizedCostMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughThree_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_DebtSecuritiesAvailableForSaleAmortizedCostMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amortized cost of investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale), with single maturity date and allocated without single maturity date, maturing in second through third fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_DebtSecuritiesAvailableForSaleAmortizedCostMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated And Single Maturity Date, After Year One Through Three</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_DebtSecuritiesAvailableForSaleAmortizedCostMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Due after one year through three years</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_DebtSecuritiesAvailableForSaleAmortizedCostMaturityAllocatedAndSingleMaturityDateAfterYearThree" xlink:label="bhm_DebtSecuritiesAvailableForSaleAmortizedCostMaturityAllocatedAndSingleMaturityDateAfterYearThree" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_DebtSecuritiesAvailableForSaleAmortizedCostMaturityAllocatedAndSingleMaturityDateAfterYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amortized cost of investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale), with single maturity date and allocated without single maturity date, maturing after third fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_DebtSecuritiesAvailableForSaleAmortizedCostMaturityAllocatedAndSingleMaturityDateAfterYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated And Single Maturity Date, After Year Three</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_DebtSecuritiesAvailableForSaleAmortizedCostMaturityAllocatedAndSingleMaturityDateAfterYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Due after three years</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Securities, Available-for-Sale, Amortized Cost</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Securities, Available-for-Sale, Maturity, Allocated and Single Maturity Date, Fair Value [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Securities, Available-for-Sale, Fair Value, Maturity, Allocated and Single Maturity Date, Year One</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Due within one year</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_DebtSecuritiesAvailableForSaleFairValueMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughThree" xlink:label="bhm_DebtSecuritiesAvailableForSaleFairValueMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughThree" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_DebtSecuritiesAvailableForSaleFairValueMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughThree" xlink:to="bhm_DebtSecuritiesAvailableForSaleFairValueMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughThree_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_DebtSecuritiesAvailableForSaleFairValueMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value of investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale), with single maturity date and allocated without single maturity date, maturing in second through third fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_DebtSecuritiesAvailableForSaleFairValueMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Securities, Available-for-Sale, Fair Value, Maturity, Allocated And Single Maturity Date, After Year One Through Three</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_DebtSecuritiesAvailableForSaleFairValueMaturityAllocatedAndSingleMaturityDateAfterYearOneThroughThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Due after one year through three years</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_DebtSecuritiesAvailableForSaleFairValueMaturityAllocatedAndSingleMaturityDateAfterYearThree" xlink:label="bhm_DebtSecuritiesAvailableForSaleFairValueMaturityAllocatedAndSingleMaturityDateAfterYearThree" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_DebtSecuritiesAvailableForSaleFairValueMaturityAllocatedAndSingleMaturityDateAfterYearThree" xlink:to="bhm_DebtSecuritiesAvailableForSaleFairValueMaturityAllocatedAndSingleMaturityDateAfterYearThree_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_DebtSecuritiesAvailableForSaleFairValueMaturityAllocatedAndSingleMaturityDateAfterYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value of investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale), with single maturity date and allocated without single maturity date, maturing after third fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_DebtSecuritiesAvailableForSaleFairValueMaturityAllocatedAndSingleMaturityDateAfterYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Securities, Available-for-Sale, Fair Value, Maturity, Allocated And Single Maturity Date, After Year Three</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_DebtSecuritiesAvailableForSaleFairValueMaturityAllocatedAndSingleMaturityDateAfterYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Due after three years</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecurities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtSecurities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecurities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Securities, Available-for-Sale</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecurities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_EncoreChandlerMember" xlink:label="bhm_EncoreChandlerMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_EncoreChandlerMember" xlink:to="bhm_EncoreChandlerMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_EncoreChandlerMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information about Encore Chandler.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_EncoreChandlerMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Chandler</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_IndigoCoveMember" xlink:label="bhm_IndigoCoveMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_IndigoCoveMember" xlink:to="bhm_IndigoCoveMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_IndigoCoveMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to Indigo Cove.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_IndigoCoveMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Indigo Cove [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_IndigoCoveMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Indigo Cove</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_CottagesAtMyrtleBeachMember" xlink:label="bhm_CottagesAtMyrtleBeachMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_CottagesAtMyrtleBeachMember" xlink:to="bhm_CottagesAtMyrtleBeachMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_CottagesAtMyrtleBeachMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to the Cottages at Myrtle Beach.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_CottagesAtMyrtleBeachMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The Cottages at Myrtle Beach [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_CottagesAtMyrtleBeachMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The Cottages at Myrtle Beach</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_CottagesOfPortSt.LucieMember" xlink:label="bhm_CottagesOfPortSt.LucieMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_CottagesOfPortSt.LucieMember" xlink:to="bhm_CottagesOfPortSt.LucieMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_CottagesOfPortSt.LucieMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information about The Cottages of Port St. Lucie.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_CottagesOfPortSt.LucieMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The Cottages of Port St. Lucie [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_CottagesOfPortSt.LucieMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The Cottages of Port St. Lucie</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_PreferredEquityInvestmentsAccruedPreferredReturns" xlink:label="bhm_PreferredEquityInvestmentsAccruedPreferredReturns" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_PreferredEquityInvestmentsAccruedPreferredReturns" xlink:to="bhm_PreferredEquityInvestmentsAccruedPreferredReturns_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_PreferredEquityInvestmentsAccruedPreferredReturns_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of accrued preferred returns on preferred equity investments.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_PreferredEquityInvestmentsAccruedPreferredReturns_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Equity Investments, Accrued Preferred Returns</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_PreferredEquityInvestmentsAccruedPreferredReturns_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrued portion of total preferred returns</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccruedInvestmentIncomeReceivable" xlink:label="us-gaap_AccruedInvestmentIncomeReceivable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccruedInvestmentIncomeReceivable" xlink:to="us-gaap_AccruedInvestmentIncomeReceivable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccruedInvestmentIncomeReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrued Investment Income Receivable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccruedInvestmentIncomeReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrued preferred equity income recorded in accounts receivable, prepaids and other assets, net</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_EquityMethodInvestmentAndJointVentureTable" xlink:label="bhm_EquityMethodInvestmentAndJointVentureTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_EquityMethodInvestmentAndJointVentureTable" xlink:to="bhm_EquityMethodInvestmentAndJointVentureTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_EquityMethodInvestmentAndJointVentureTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment And Joint Venture [Table]</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_ArcherAtRiverblueCanvasAtWildwoodRiverFordAndSanfordMarketplaceMember" xlink:label="bhm_ArcherAtRiverblueCanvasAtWildwoodRiverFordAndSanfordMarketplaceMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_ArcherAtRiverblueCanvasAtWildwoodRiverFordAndSanfordMarketplaceMember" xlink:to="bhm_ArcherAtRiverblueCanvasAtWildwoodRiverFordAndSanfordMarketplaceMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_ArcherAtRiverblueCanvasAtWildwoodRiverFordAndSanfordMarketplaceMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Archer at RiverBlue, Canvas at Wildwood, River Ford, and Sanford Marketplace.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_ArcherAtRiverblueCanvasAtWildwoodRiverFordAndSanfordMarketplaceMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Archer at RiverBlue, Canvas at Wildwood, River Ford, and Sanford Marketplace [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_ArcherAtRiverblueCanvasAtWildwoodRiverFordAndSanfordMarketplaceMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Archer at RiverBlue, Canvas at Wildwood, River Ford, and Sanford Marketplace</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_EquityMethodInvestmentAndJointVentureLineItems" xlink:label="bhm_EquityMethodInvestmentAndJointVentureLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_EquityMethodInvestmentAndJointVentureLineItems" xlink:to="bhm_EquityMethodInvestmentAndJointVentureLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_EquityMethodInvestmentAndJointVentureLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_EquityMethodInvestmentAndJointVentureLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment And Joint Venture [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bhm_EquityMethodInvestmentAndJointVentureLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Equity Investments</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_DebtSecuritiesAvailableForSaleGross" xlink:label="bhm_DebtSecuritiesAvailableForSaleGross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_DebtSecuritiesAvailableForSaleGross" xlink:to="bhm_DebtSecuritiesAvailableForSaleGross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_DebtSecuritiesAvailableForSaleGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount before unrealized gains or losses of investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_DebtSecuritiesAvailableForSaleGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Securities, Available-for-Sale, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bhm_DebtSecuritiesAvailableForSaleGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total investment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireEquityMethodInvestments" xlink:label="us-gaap_PaymentsToAcquireEquityMethodInvestments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsToAcquireEquityMethodInvestments" xlink:to="us-gaap_PaymentsToAcquireEquityMethodInvestments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsToAcquireEquityMethodInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments to acquire investment commitment amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PaymentsToAcquireEquityMethodInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment purchase price</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_CommitmentToInvestInPreferredEquityInterests" xlink:label="bhm_CommitmentToInvestInPreferredEquityInterests" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_CommitmentToInvestInPreferredEquityInterests" xlink:to="bhm_CommitmentToInvestInPreferredEquityInterests_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_CommitmentToInvestInPreferredEquityInterests_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of commitment to invest in preferred equity interests.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_CommitmentToInvestInPreferredEquityInterests_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commitment to Invest in Preferred Equity Interests</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_CommitmentToInvestInPreferredEquityInterests_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of commitment to invest in preferred equity interests</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bhm_CommitmentToInvestInPreferredEquityInterests_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of commitment to invest in preferred equity interests</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_PrivatePlacementOfferingProgramTable" xlink:label="bhm_PrivatePlacementOfferingProgramTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_PrivatePlacementOfferingProgramTable" xlink:to="bhm_PrivatePlacementOfferingProgramTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_PrivatePlacementOfferingProgramTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The disclosure of information pertaining to the private placement offering program of the entity during the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_PrivatePlacementOfferingProgramTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Private Placement Offering Program [Table]</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_PrivatePlacementOfferingProgramLineItems" xlink:label="bhm_PrivatePlacementOfferingProgramLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_PrivatePlacementOfferingProgramLineItems" xlink:to="bhm_PrivatePlacementOfferingProgramLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_PrivatePlacementOfferingProgramLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_PrivatePlacementOfferingProgramLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Private Placement Offering Program [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_PrivatePlacementOfferingProgramLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">DST Program</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_DstProgramPurchaseOptionInTrustAtFairValuePeriodFromFullSyndication" xlink:label="bhm_DstProgramPurchaseOptionInTrustAtFairValuePeriodFromFullSyndication" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_DstProgramPurchaseOptionInTrustAtFairValuePeriodFromFullSyndication" xlink:to="bhm_DstProgramPurchaseOptionInTrustAtFairValuePeriodFromFullSyndication_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_DstProgramPurchaseOptionInTrustAtFairValuePeriodFromFullSyndication_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The time period from the full syndication within which the purchase option can be exercised to acquire the interests of the Delaware Statutory Trust at fair value by the entity.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_DstProgramPurchaseOptionInTrustAtFairValuePeriodFromFullSyndication_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">DST Program, Purchase Option In Trust At Fair Value, Period From Full Syndication</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_DstProgramPurchaseOptionInTrustAtFairValuePeriodFromFullSyndication_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Time period from the full syndication</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_DstProgramNetProceedsFromIssuanceOfBeneficialInterestsInPrivateOfferings" xlink:label="bhm_DstProgramNetProceedsFromIssuanceOfBeneficialInterestsInPrivateOfferings" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_DstProgramNetProceedsFromIssuanceOfBeneficialInterestsInPrivateOfferings" xlink:to="bhm_DstProgramNetProceedsFromIssuanceOfBeneficialInterestsInPrivateOfferings_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_DstProgramNetProceedsFromIssuanceOfBeneficialInterestsInPrivateOfferings_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The cash inflow from the issuance of beneficial interests of the Delaware Statutory Trusts through private placement offerings during the reporting period, net.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_DstProgramNetProceedsFromIssuanceOfBeneficialInterestsInPrivateOfferings_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">DST Program, Net Proceeds From Issuance Of Beneficial Interests In Private Offerings</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_DstProgramNetProceedsFromIssuanceOfBeneficialInterestsInPrivateOfferings_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Offering Proceeds Raised</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_DstProgramNetRealEstateInvestments" xlink:label="bhm_DstProgramNetRealEstateInvestments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_DstProgramNetRealEstateInvestments" xlink:to="bhm_DstProgramNetRealEstateInvestments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_DstProgramNetRealEstateInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of total net real estate investments associated with the Delaware Statutory Trust Program as of the reporting date.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_DstProgramNetRealEstateInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">DST Program, Net Real Estate Investments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_DstProgramNetRealEstateInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Real Estate Investments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditFacilityTable" xlink:label="us-gaap_LineOfCreditFacilityTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LineOfCreditFacilityTable" xlink:to="us-gaap_LineOfCreditFacilityTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LineOfCreditFacilityTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line of Credit Facility [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CreditFacilityAxis" xlink:label="us-gaap_CreditFacilityAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CreditFacilityAxis" xlink:to="us-gaap_CreditFacilityAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CreditFacilityAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Credit Facility [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CreditFacilityDomain" xlink:label="us-gaap_CreditFacilityDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CreditFacilityDomain" xlink:to="us-gaap_CreditFacilityDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CreditFacilityDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Credit Facility [Domain]</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_KeybankCreditFacilityMember" xlink:label="bhm_KeybankCreditFacilityMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_KeybankCreditFacilityMember" xlink:to="bhm_KeybankCreditFacilityMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_KeybankCreditFacilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Keybank credit facility.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_KeybankCreditFacilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">KeyBank Credit Facility [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_KeybankCreditFacilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">KeyBank Credit Facility</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariableRateAxis" xlink:label="us-gaap_VariableRateAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_VariableRateAxis" xlink:to="us-gaap_VariableRateAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_VariableRateAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Variable Rate [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariableRateDomain" xlink:label="us-gaap_VariableRateDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_VariableRateDomain" xlink:to="us-gaap_VariableRateDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_VariableRateDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Variable Rate [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SecuredOvernightFinancingRateSofrMember" xlink:label="us-gaap_SecuredOvernightFinancingRateSofrMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SecuredOvernightFinancingRateSofrMember" xlink:to="us-gaap_SecuredOvernightFinancingRateSofrMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SecuredOvernightFinancingRateSofrMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Secured Overnight Financing Rate Sofr Overnight Index Swap Rate [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SecuredOvernightFinancingRateSofrMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SOFR</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BaseRateMember" xlink:label="us-gaap_BaseRateMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BaseRateMember" xlink:to="us-gaap_BaseRateMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BaseRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Base Rate [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BaseRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Base Rate</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FederalFundsEffectiveSwapRateMember" xlink:label="us-gaap_FederalFundsEffectiveSwapRateMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FederalFundsEffectiveSwapRateMember" xlink:to="us-gaap_FederalFundsEffectiveSwapRateMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FederalFundsEffectiveSwapRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fed Funds Effective Rate Overnight Index Swap Rate [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FederalFundsEffectiveSwapRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Federal funds effective rate</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_AdjustedSecuredOvernightFinancingRateSofrMember" xlink:label="bhm_AdjustedSecuredOvernightFinancingRateSofrMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_AdjustedSecuredOvernightFinancingRateSofrMember" xlink:to="bhm_AdjustedSecuredOvernightFinancingRateSofrMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_AdjustedSecuredOvernightFinancingRateSofrMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents adjusted secured overnight financing rate (SOFR).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_AdjustedSecuredOvernightFinancingRateSofrMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjusted Secured Overnight Financing Rate (SOFR) [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_AdjustedSecuredOvernightFinancingRateSofrMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjusted Term SOFR</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditFacilityLineItems" xlink:label="us-gaap_LineOfCreditFacilityLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LineOfCreditFacilityLineItems" xlink:to="us-gaap_LineOfCreditFacilityLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LineOfCreditFacilityLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line of Credit Facility [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LineOfCreditFacilityLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Mortgages Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_LineOfCreditFacilityLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revolving Credit Facilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:to="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line of Credit Facility, Maximum Borrowing Capacity</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum total commitment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:to="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Basis Spread on Variable Rate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Spread on variable interest rate (as a percent)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage" xlink:label="us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage" xlink:to="us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line of Credit Facility, Unused Capacity, Commitment Fee Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unused fee (as a percent)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCredit" xlink:label="us-gaap_LineOfCredit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LineOfCredit" xlink:to="us-gaap_LineOfCredit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LineOfCredit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-term Line of Credit</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_LineOfCredit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Outstanding balance</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_DbLoanMember" xlink:label="bhm_DbLoanMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_DbLoanMember" xlink:to="bhm_DbLoanMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_DbLoanMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to DB Loan.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_DbLoanMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">DB Loan [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_DbLoanMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">DB Loan</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeAxis" xlink:label="us-gaap_LongtermDebtTypeAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongtermDebtTypeAxis" xlink:to="us-gaap_LongtermDebtTypeAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongtermDebtTypeAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-term Debt, Type [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeDomain" xlink:label="us-gaap_LongtermDebtTypeDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongtermDebtTypeDomain" xlink:to="us-gaap_LongtermDebtTypeDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongtermDebtTypeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-term Debt, Type [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MortgagesMember" xlink:label="us-gaap_MortgagesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MortgagesMember" xlink:to="us-gaap_MortgagesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MortgagesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Mortgages [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MortgagesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Mortgages</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_InterestRateByTypeAxis" xlink:label="bhm_InterestRateByTypeAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_InterestRateByTypeAxis" xlink:to="bhm_InterestRateByTypeAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_InterestRateByTypeAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Information by type of interest rate.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_InterestRateByTypeAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Rate By Type [Axis]</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_InterestRateByTypeDomain" xlink:label="bhm_InterestRateByTypeDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_InterestRateByTypeDomain" xlink:to="bhm_InterestRateByTypeDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_InterestRateByTypeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest rate type.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_InterestRateByTypeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Rate By Type [Domain]</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_FixedInterestRateMember" xlink:label="bhm_FixedInterestRateMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_FixedInterestRateMember" xlink:to="bhm_FixedInterestRateMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_FixedInterestRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to fixed interest rate.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_FixedInterestRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fixed Interest Rate [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_FixedInterestRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fixed Rate</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_FloatingInterestRateMember" xlink:label="bhm_FloatingInterestRateMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_FloatingInterestRateMember" xlink:to="bhm_FloatingInterestRateMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_FloatingInterestRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to floating interest rate.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_FloatingInterestRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Floating Interest Rate [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_FloatingInterestRateMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Floating Rate</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SecuredDebt" xlink:label="us-gaap_SecuredDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SecuredDebt" xlink:to="us-gaap_SecuredDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SecuredDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Secured Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SecuredDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Outstanding Principal</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:to="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Interest Rate, Stated Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest rate on outstanding borrowings (as a percent)</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_MortgagesPayable" xlink:label="bhm_MortgagesPayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_MortgagesPayable" xlink:to="bhm_MortgagesPayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_MortgagesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carrying value as of the balance sheet date of total mortgages payable.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_MortgagesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Mortgages Payable.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_MortgagesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet" xlink:to="us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Unamortized Discount (Premium), Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscountPremiumNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value adjustments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredFinanceCostsNet" xlink:label="us-gaap_DeferredFinanceCostsNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DeferredFinanceCostsNet" xlink:to="us-gaap_DeferredFinanceCostsNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Issuance Costs, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred financing costs, net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subtract: Deferred financing costs, net</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_MortgagesPayableExcludingPayablesHeldForSale" xlink:label="bhm_MortgagesPayableExcludingPayablesHeldForSale" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_MortgagesPayableExcludingPayablesHeldForSale" xlink:to="bhm_MortgagesPayableExcludingPayablesHeldForSale_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_MortgagesPayableExcludingPayablesHeldForSale_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carrying value as of the balance sheet date of mortgages payable, excluding payables held for sale.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_MortgagesPayableExcludingPayablesHeldForSale_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Mortgages Payable, Excluding Payables Held For Sale</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_MortgagesPayableExcludingPayablesHeldForSale_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total mortgages payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortTermDebtTypeAxis" xlink:label="us-gaap_ShortTermDebtTypeAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShortTermDebtTypeAxis" xlink:to="us-gaap_ShortTermDebtTypeAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShortTermDebtTypeAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Short-term Debt, Type [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortTermDebtTypeDomain" xlink:label="us-gaap_ShortTermDebtTypeDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShortTermDebtTypeDomain" xlink:to="us-gaap_ShortTermDebtTypeDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShortTermDebtTypeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Short-term Debt, Type [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditMember" xlink:label="us-gaap_LineOfCreditMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LineOfCreditMember" xlink:to="us-gaap_LineOfCreditMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LineOfCreditMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line Of Credit [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LineOfCreditMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line of Credit</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_CreditAgreementOneMember" xlink:label="bhm_CreditAgreementOneMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_CreditAgreementOneMember" xlink:to="bhm_CreditAgreementOneMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_CreditAgreementOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to one credit agreements.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_CreditAgreementOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Credit Agreement One [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_CreditAgreementOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">One credit agreement</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_CreditAgreementsTwoMember" xlink:label="bhm_CreditAgreementsTwoMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_CreditAgreementsTwoMember" xlink:to="bhm_CreditAgreementsTwoMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_CreditAgreementsTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">A contractual arrangement with a lender under which borrowings can be made up to a specific amount at any point in time, and under which borrowings outstanding may be either short-term or long-term, depending upon the particulars.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_CreditAgreementsTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Credit Agreements Two [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_CreditAgreementsTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Second credit agreement</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SeniorLoansMember" xlink:label="us-gaap_SeniorLoansMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SeniorLoansMember" xlink:to="us-gaap_SeniorLoansMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SeniorLoansMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Senior Loans [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SeniorLoansMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Senior loan</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_SupplementalLoanMember" xlink:label="bhm_SupplementalLoanMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_SupplementalLoanMember" xlink:to="bhm_SupplementalLoanMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_SupplementalLoanMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to supplemental loan.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_SupplementalLoanMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Supplemental Loan [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_SupplementalLoanMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Supplemental loan</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeAxis" xlink:label="srt_RangeAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RangeAxis" xlink:to="srt_RangeAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_RangeAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Range [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember" xlink:label="srt_RangeMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RangeMember" xlink:to="srt_RangeMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_RangeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Range [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MinimumMember" xlink:label="srt_MinimumMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_MinimumMember" xlink:to="srt_MinimumMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_MinimumMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_MinimumMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MaximumMember" xlink:label="srt_MaximumMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_MaximumMember" xlink:to="srt_MaximumMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_MaximumMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_MaximumMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SecuredLongTermDebt" xlink:label="us-gaap_SecuredLongTermDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SecuredLongTermDebt" xlink:to="us-gaap_SecuredLongTermDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SecuredLongTermDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Secured Long-term Debt, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SecuredLongTermDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Principal balance</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentVariableInterestRateTypeExtensibleEnumeration" xlink:label="us-gaap_DebtInstrumentVariableInterestRateTypeExtensibleEnumeration" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentVariableInterestRateTypeExtensibleEnumeration" xlink:to="us-gaap_DebtInstrumentVariableInterestRateTypeExtensibleEnumeration_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentVariableInterestRateTypeExtensibleEnumeration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Variable Interest Rate, Type [Extensible Enumeration]</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_DebtInstrumentReferenceRate" xlink:label="bhm_DebtInstrumentReferenceRate" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_DebtInstrumentReferenceRate" xlink:to="bhm_DebtInstrumentReferenceRate_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_DebtInstrumentReferenceRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reference rate to compute the variable rate on the debt instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_DebtInstrumentReferenceRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument Reference Rate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_DebtInstrumentReferenceRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reference rate</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AmortizationOfFinancingCosts" xlink:label="us-gaap_AmortizationOfFinancingCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AmortizationOfFinancingCosts" xlink:to="us-gaap_AmortizationOfFinancingCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AmortizationOfFinancingCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amortization of Debt Issuance Costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AmortizationOfFinancingCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amortization of deferred financing costs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentCollateralAmount" xlink:label="us-gaap_DebtInstrumentCollateralAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentCollateralAmount" xlink:to="us-gaap_DebtInstrumentCollateralAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentCollateralAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Collateral Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentCollateralAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net book value of real estate assets providing collateral</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_MortgagesPayableAbstract" xlink:label="bhm_MortgagesPayableAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_MortgagesPayableAbstract" xlink:to="bhm_MortgagesPayableAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_MortgagesPayableAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Mortgages Payable [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_MortgagesPayableAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Mortgages Payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:to="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Debt, Maturity, Remainder of Fiscal Year</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2026</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:to="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-term Debt, Maturities, Repayments of Principal in Next Twelve Months</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:to="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-term Debt, Maturities, Repayments of Principal in Year Two</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2028</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:to="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-term Debt, Maturities, Repayments of Principal in Year Three</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2029</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:to="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-term Debt, Maturities, Repayments of Principal in Year Four</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2030</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_LongTermDebtMaturityAfterYearFour" xlink:label="bhm_LongTermDebtMaturityAfterYearFour" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_LongTermDebtMaturityAfterYearFour" xlink:to="bhm_LongTermDebtMaturityAfterYearFour_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_LongTermDebtMaturityAfterYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of long-term debt payable, sinking fund requirement, and other securities issued that are redeemable by holder at fixed or determinable price and date, maturing after fifth fourth year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_LongTermDebtMaturityAfterYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Debt, Maturity, after Year Four</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_LongTermDebtMaturityAfterYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Thereafter</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentCarryingAmount" xlink:label="us-gaap_DebtInstrumentCarryingAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentCarryingAmount" xlink:to="us-gaap_DebtInstrumentCarryingAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-term Debt, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Mortgages before adjustments for deferred financing costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-term Debt</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentUnamortizedDiscount" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentUnamortizedDiscount" xlink:to="us-gaap_DebtInstrumentUnamortizedDiscount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Unamortized Discount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Add: Unamortized fair value debt adjustment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebt" xlink:label="us-gaap_LongTermDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebt" xlink:to="us-gaap_LongTermDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-term Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_LongTermDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total mortgages payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByBalanceSheetGroupingTable" xlink:label="us-gaap_FairValueByBalanceSheetGroupingTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueByBalanceSheetGroupingTable" xlink:to="us-gaap_FairValueByBalanceSheetGroupingTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueByBalanceSheetGroupingTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, by Balance Sheet Grouping [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByMeasurementBasisAxis" xlink:label="us-gaap_FairValueByMeasurementBasisAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueByMeasurementBasisAxis" xlink:to="us-gaap_FairValueByMeasurementBasisAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueByMeasurementBasisAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Basis [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:label="us-gaap_PortionAtFairValueFairValueDisclosureMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:to="us-gaap_PortionAtFairValueFairValueDisclosureMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PortionAtFairValueFairValueDisclosureMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Portion at Fair Value Measurement [Member]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:label="us-gaap_CarryingReportedAmountFairValueDisclosureMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:to="us-gaap_CarryingReportedAmountFairValueDisclosureMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CarryingReportedAmountFairValueDisclosureMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reported Value Measurement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CarryingReportedAmountFairValueDisclosureMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carrying Value</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:label="us-gaap_EstimateOfFairValueFairValueDisclosureMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:to="us-gaap_EstimateOfFairValueFairValueDisclosureMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EstimateOfFairValueFairValueDisclosureMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Estimate of Fair Value Measurement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EstimateOfFairValueFairValueDisclosureMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Hierarchy and NAV [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel3Member" xlink:label="us-gaap_FairValueInputsLevel3Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueInputsLevel3Member" xlink:to="us-gaap_FairValueInputsLevel3Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Inputs, Level 3 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Level 3</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel2Member" xlink:label="us-gaap_FairValueInputsLevel2Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueInputsLevel2Member" xlink:to="us-gaap_FairValueInputsLevel2Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueInputsLevel2Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Inputs, Level 2 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueInputsLevel2Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Level 2</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:label="us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:to="us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsFairValueDisclosureAbstract" xlink:label="us-gaap_AssetsFairValueDisclosureAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsFairValueDisclosureAbstract" xlink:to="us-gaap_AssetsFairValueDisclosureAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetsFairValueDisclosureAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Assets, Fair Value Disclosure [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetsFairValueDisclosureAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Assets</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MortgageBackedSecuritiesAvailableForSaleFairValueDisclosure" xlink:to="us-gaap_MortgageBackedSecuritiesAvailableForSaleFairValueDisclosure_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MortgageBackedSecuritiesAvailableForSaleFairValueDisclosure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Security, Mortgage-Backed, Available-for-Sale, Fair Value Disclosure</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MortgageBackedSecuritiesAvailableForSaleFairValueDisclosure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred equity investments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeAssetsCurrent" xlink:label="us-gaap_DerivativeAssetsCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeAssetsCurrent" xlink:to="us-gaap_DerivativeAssetsCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeAssetsCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Asset, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeAssetsCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative financial instruments</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_DerivativeAssetCurrentStatementOfFinancialPositionExtensibleEnumerationNotDisclosedFlag" xlink:label="bhm_DerivativeAssetCurrentStatementOfFinancialPositionExtensibleEnumerationNotDisclosedFlag" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_DerivativeAssetCurrentStatementOfFinancialPositionExtensibleEnumerationNotDisclosedFlag" xlink:to="bhm_DerivativeAssetCurrentStatementOfFinancialPositionExtensibleEnumerationNotDisclosedFlag_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_DerivativeAssetCurrentStatementOfFinancialPositionExtensibleEnumerationNotDisclosedFlag_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Boolean flag that is true when the XBRL content not disclosed in Face Financials.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_DerivativeAssetCurrentStatementOfFinancialPositionExtensibleEnumerationNotDisclosedFlag_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Asset Current Statement Of Financial Position Extensible Enumeration Not Disclosed [Flag]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:to="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Recurring and Nonrecurring [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByMeasurementFrequencyAxis" xlink:label="us-gaap_FairValueByMeasurementFrequencyAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueByMeasurementFrequencyAxis" xlink:to="us-gaap_FairValueByMeasurementFrequencyAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueByMeasurementFrequencyAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Frequency [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementFrequencyDomain" xlink:label="us-gaap_FairValueMeasurementFrequencyDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueMeasurementFrequencyDomain" xlink:to="us-gaap_FairValueMeasurementFrequencyDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueMeasurementFrequencyDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Frequency [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsNonrecurringMember" xlink:label="us-gaap_FairValueMeasurementsNonrecurringMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueMeasurementsNonrecurringMember" xlink:to="us-gaap_FairValueMeasurementsNonrecurringMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueMeasurementsNonrecurringMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Nonrecurring [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueMeasurementsNonrecurringMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-Recurring</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_RealEstateHeldForSaleBeforeImpairment" xlink:label="bhm_RealEstateHeldForSaleBeforeImpairment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_RealEstateHeldForSaleBeforeImpairment" xlink:to="bhm_RealEstateHeldForSaleBeforeImpairment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_RealEstateHeldForSaleBeforeImpairment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents amount of investment in real estate property held for sale before impairment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_RealEstateHeldForSaleBeforeImpairment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Real Estate, Held For Sale Before Impairment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_RealEstateHeldForSaleBeforeImpairment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Pre-impairment amount</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsHeldForSaleLongLivedFairValueDisclosure" xlink:label="us-gaap_AssetsHeldForSaleLongLivedFairValueDisclosure" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsHeldForSaleLongLivedFairValueDisclosure" xlink:to="us-gaap_AssetsHeldForSaleLongLivedFairValueDisclosure_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetsHeldForSaleLongLivedFairValueDisclosure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Lived Asset, Held-for-Sale, Fair Value Disclosure</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AssetsHeldForSaleLongLivedFairValueDisclosure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable" xlink:label="us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable" xlink:to="us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Instruments, Gain (Loss) [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeInstrumentRiskAxis" xlink:label="us-gaap_DerivativeInstrumentRiskAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeInstrumentRiskAxis" xlink:to="us-gaap_DerivativeInstrumentRiskAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeInstrumentRiskAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Instrument [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeContractTypeDomain" xlink:label="us-gaap_DerivativeContractTypeDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeContractTypeDomain" xlink:to="us-gaap_DerivativeContractTypeDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeContractTypeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Contract [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestRateCapMember" xlink:label="us-gaap_InterestRateCapMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestRateCapMember" xlink:to="us-gaap_InterestRateCapMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InterestRateCapMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Rate Cap [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InterestRateCapMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest rate caps</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestRateSwapMember" xlink:label="us-gaap_InterestRateSwapMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestRateSwapMember" xlink:to="us-gaap_InterestRateSwapMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InterestRateSwapMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Rate Swap [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InterestRateSwapMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest rate swaps</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTypeAxis" xlink:label="us-gaap_SubsequentEventTypeAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventTypeAxis" xlink:to="us-gaap_SubsequentEventTypeAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventTypeAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent Event Type [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTypeDomain" xlink:label="us-gaap_SubsequentEventTypeDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventTypeDomain" xlink:to="us-gaap_SubsequentEventTypeDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventMember" xlink:label="us-gaap_SubsequentEventMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventMember" xlink:to="us-gaap_SubsequentEventMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent Events [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SubsequentEventMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent events</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:label="us-gaap_DerivativeInstrumentsGainLossLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:to="us-gaap_DerivativeInstrumentsGainLossLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeInstrumentsGainLossLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Instruments, Gain (Loss) [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeInstrumentsGainLossLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Financial Instruments</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_AmountOfDebtCoveredByDerivatives" xlink:label="bhm_AmountOfDebtCoveredByDerivatives" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_AmountOfDebtCoveredByDerivatives" xlink:to="bhm_AmountOfDebtCoveredByDerivatives_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_AmountOfDebtCoveredByDerivatives_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The total amount of variable debt covered by the derivatives.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_AmountOfDebtCoveredByDerivatives_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount Of Debt Covered By Derivatives</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_AmountOfDebtCoveredByDerivatives_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of debt covered by derivatives</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeNotionalAmount" xlink:label="us-gaap_DerivativeNotionalAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeNotionalAmount" xlink:to="us-gaap_DerivativeNotionalAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeNotionalAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative, Notional Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeNotionalAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notional balance</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeNumberOfInstrumentsHeld" xlink:label="us-gaap_DerivativeNumberOfInstrumentsHeld" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeNumberOfInstrumentsHeld" xlink:to="us-gaap_DerivativeNumberOfInstrumentsHeld_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeNumberOfInstrumentsHeld_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative, Number of Instruments Held</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeNumberOfInstrumentsHeld_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of instruments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestRateDerivativeInstrumentsNotDesignatedAsHedgingInstrumentsAssetAtFairValue" xlink:label="us-gaap_InterestRateDerivativeInstrumentsNotDesignatedAsHedgingInstrumentsAssetAtFairValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestRateDerivativeInstrumentsNotDesignatedAsHedgingInstrumentsAssetAtFairValue" xlink:to="us-gaap_InterestRateDerivativeInstrumentsNotDesignatedAsHedgingInstrumentsAssetAtFairValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InterestRateDerivativeInstrumentsNotDesignatedAsHedgingInstrumentsAssetAtFairValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Rate Derivative Instruments Not Designated as Hedging Instruments, Asset at Fair Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InterestRateDerivativeInstrumentsNotDesignatedAsHedgingInstrumentsAssetAtFairValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Values of derivative</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeGainLossOnDerivativeNet" xlink:label="us-gaap_DerivativeGainLossOnDerivativeNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeGainLossOnDerivativeNet" xlink:to="us-gaap_DerivativeGainLossOnDerivativeNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeGainLossOnDerivativeNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative, Gain (Loss) on Derivative, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_DerivativeGainLossOnDerivativeNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on derivatives</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeGainLossStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration" xlink:label="us-gaap_DerivativeGainLossStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeGainLossStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration" xlink:to="us-gaap_DerivativeGainLossStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeGainLossStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative, Gain (Loss), Statement of Income or Comprehensive Income [Extensible Enumeration]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related Party [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyDomain" xlink:label="us-gaap_RelatedPartyDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyDomain" xlink:to="us-gaap_RelatedPartyDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related Party [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyMember" xlink:label="us-gaap_RelatedPartyMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyMember" xlink:to="us-gaap_RelatedPartyMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related Party [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RelatedPartyMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related Party</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionAxis" xlink:label="us-gaap_RelatedPartyTransactionAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionAxis" xlink:to="us-gaap_RelatedPartyTransactionAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyTransactionAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related Party Transaction [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionDomain" xlink:label="us-gaap_RelatedPartyTransactionDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionDomain" xlink:to="us-gaap_RelatedPartyTransactionDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyTransactionDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related Party Transaction [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ManagementServiceBaseMember" xlink:label="us-gaap_ManagementServiceBaseMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ManagementServiceBaseMember" xlink:to="us-gaap_ManagementServiceBaseMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ManagementServiceBaseMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Management Service, Base [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ManagementServiceBaseMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Base management fee</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_ManagementServiceBasePayableInKindMember" xlink:label="bhm_ManagementServiceBasePayableInKindMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_ManagementServiceBasePayableInKindMember" xlink:to="bhm_ManagementServiceBasePayableInKindMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_ManagementServiceBasePayableInKindMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Portion payable in kind of contractually stipulated right to receive base compensation for operating and managing business.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_ManagementServiceBasePayableInKindMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Management Service Base Payable In Kind [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_ManagementServiceBasePayableInKindMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Base management fee, payable in kind</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ManagementServiceIncentiveMember" xlink:label="us-gaap_ManagementServiceIncentiveMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ManagementServiceIncentiveMember" xlink:to="us-gaap_ManagementServiceIncentiveMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ManagementServiceIncentiveMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Management Service, Incentive [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ManagementServiceIncentiveMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Incentive fee</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_OperatingAndDirectExpenseReimbursementsMember" xlink:label="bhm_OperatingAndDirectExpenseReimbursementsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_OperatingAndDirectExpenseReimbursementsMember" xlink:to="bhm_OperatingAndDirectExpenseReimbursementsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_OperatingAndDirectExpenseReimbursementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to operating and direct expense reimbursements.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_OperatingAndDirectExpenseReimbursementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating And Direct Expense Reimbursements [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_OperatingAndDirectExpenseReimbursementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating and direct expense reimbursements</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_OperatingExpenseReimbursementsMember" xlink:label="bhm_OperatingExpenseReimbursementsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_OperatingExpenseReimbursementsMember" xlink:to="bhm_OperatingExpenseReimbursementsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_OperatingExpenseReimbursementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Information pertaining to operating expense reimbursements.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_OperatingExpenseReimbursementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Expense Reimbursements [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_OperatingExpenseReimbursementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating expense reimbursements</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_DirectExpenseReimbursementsMember" xlink:label="bhm_DirectExpenseReimbursementsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_DirectExpenseReimbursementsMember" xlink:to="bhm_DirectExpenseReimbursementsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_DirectExpenseReimbursementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Information pertaining to direct expense reimbursements.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_DirectExpenseReimbursementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Direct Expense Reimbursements [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_DirectExpenseReimbursementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Direct expense reimbursements</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_StockOfferingCostsMember" xlink:label="bhm_StockOfferingCostsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_StockOfferingCostsMember" xlink:to="bhm_StockOfferingCostsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_StockOfferingCostsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Information pertaining to stock offering costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_StockOfferingCostsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Offering Costs [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_StockOfferingCostsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock offering costs</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_AgreementRenewalTerm" xlink:label="bhm_AgreementRenewalTerm" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_AgreementRenewalTerm" xlink:to="bhm_AgreementRenewalTerm_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_AgreementRenewalTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the renewal term of agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_AgreementRenewalTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Agreement, Renewal Term</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_AgreementRenewalTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Renewal term (in years)</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_PercentageOfBaseManagementFee" xlink:label="bhm_PercentageOfBaseManagementFee" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_PercentageOfBaseManagementFee" xlink:to="bhm_PercentageOfBaseManagementFee_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_PercentageOfBaseManagementFee_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the percentage of Base Management Fee.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_PercentageOfBaseManagementFee_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of Base Management Fee</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_PercentageOfBaseManagementFee_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Base management fee (as a percent)</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_ManagementFeeExpenseRelatedPartyPaidInKind" xlink:label="bhm_ManagementFeeExpenseRelatedPartyPaidInKind" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_ManagementFeeExpenseRelatedPartyPaidInKind" xlink:to="bhm_ManagementFeeExpenseRelatedPartyPaidInKind_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_ManagementFeeExpenseRelatedPartyPaidInKind_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of expense for investment management fee, including, but not limited to, expense in connection with research, selection, supervision, and custody of investment. with related parties that are settled through payments in kind by the entity during the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_ManagementFeeExpenseRelatedPartyPaidInKind_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Management Fee Expense, Related Party, Paid In Kind</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_ManagementFeeExpenseRelatedPartyPaidInKind_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Management Fee Expense</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:label="us-gaap_RelatedPartyTransactionAmountsOfTransaction" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:to="us-gaap_RelatedPartyTransactionAmountsOfTransaction_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyTransactionAmountsOfTransaction_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related Party Transaction, Amounts of Transaction</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RelatedPartyTransactionAmountsOfTransaction_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of related party transaction during the period</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_ReimbursementOfOperatingCosts" xlink:label="bhm_ReimbursementOfOperatingCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_ReimbursementOfOperatingCosts" xlink:to="bhm_ReimbursementOfOperatingCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_ReimbursementOfOperatingCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the amount of reimbursement of operating costs.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_ReimbursementOfOperatingCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reimbursement of Operating Costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_ReimbursementOfOperatingCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reimbursement of operating costs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_CounterpartyNameAxis" xlink:label="srt_CounterpartyNameAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_CounterpartyNameAxis" xlink:to="srt_CounterpartyNameAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_CounterpartyNameAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Counterparty Name [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RepurchaseAgreementCounterpartyNameDomain" xlink:label="srt_RepurchaseAgreementCounterpartyNameDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RepurchaseAgreementCounterpartyNameDomain" xlink:to="srt_RepurchaseAgreementCounterpartyNameDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_RepurchaseAgreementCounterpartyNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Counterparty Name [Domain]</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_BluerockHomesManagerLlcMember" xlink:label="bhm_BluerockHomesManagerLlcMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_BluerockHomesManagerLlcMember" xlink:to="bhm_BluerockHomesManagerLlcMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_BluerockHomesManagerLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Bluerock Homes Manager, LLC.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_BluerockHomesManagerLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Bluerock Homes Manager, Llc [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_BluerockHomesManagerLlcMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Bluerock Homes Manager, LLC</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetManagement1Member" xlink:label="us-gaap_AssetManagement1Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetManagement1Member" xlink:to="us-gaap_AssetManagement1Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetManagement1Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Management [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetManagement1Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset management fee</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_OneTimeAssetAcquisitionFeeMember" xlink:label="bhm_OneTimeAssetAcquisitionFeeMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_OneTimeAssetAcquisitionFeeMember" xlink:to="bhm_OneTimeAssetAcquisitionFeeMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_OneTimeAssetAcquisitionFeeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to one-time asset  acquisition fees.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_OneTimeAssetAcquisitionFeeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">One Time Asset Acquisition Fee [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_OneTimeAssetAcquisitionFeeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">One-time acquisition fee</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromIssuanceOfLongTermDebt" xlink:label="us-gaap_ProceedsFromIssuanceOfLongTermDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromIssuanceOfLongTermDebt" xlink:to="us-gaap_ProceedsFromIssuanceOfLongTermDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromIssuanceOfLongTermDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Issuance of Long-Term Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromIssuanceOfLongTermDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_NoncontrollingInterestContributionFromAffiliateForRealEstateAcquisition" xlink:label="bhm_NoncontrollingInterestContributionFromAffiliateForRealEstateAcquisition" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_NoncontrollingInterestContributionFromAffiliateForRealEstateAcquisition" xlink:to="bhm_NoncontrollingInterestContributionFromAffiliateForRealEstateAcquisition_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_NoncontrollingInterestContributionFromAffiliateForRealEstateAcquisition_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of equity contributed by an affiliate of the manager representing a noncontrolling interest in a real estate investment in connection with a property acquisition.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_NoncontrollingInterestContributionFromAffiliateForRealEstateAcquisition_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling Interest Contribution from Affiliate for Real Estate Acquisition</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_NoncontrollingInterestContributionFromAffiliateForRealEstateAcquisition_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity contributed</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_RelatedPartyAmountsRelatedToUnconsolidatedRealEstateFundAgreementMember" xlink:label="bhm_RelatedPartyAmountsRelatedToUnconsolidatedRealEstateFundAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_RelatedPartyAmountsRelatedToUnconsolidatedRealEstateFundAgreementMember" xlink:to="bhm_RelatedPartyAmountsRelatedToUnconsolidatedRealEstateFundAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_RelatedPartyAmountsRelatedToUnconsolidatedRealEstateFundAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Information pertaining to related party transactions from the unconsolidated real estate funds.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_RelatedPartyAmountsRelatedToUnconsolidatedRealEstateFundAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related Party Amounts Related To Unconsolidated Real Estate Fund Agreement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_RelatedPartyAmountsRelatedToUnconsolidatedRealEstateFundAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unconsolidated Real Estate Fund</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_CarriedInterestRelatedToUnconsolidatedRealEstateFundMember" xlink:label="bhm_CarriedInterestRelatedToUnconsolidatedRealEstateFundMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_CarriedInterestRelatedToUnconsolidatedRealEstateFundMember" xlink:to="bhm_CarriedInterestRelatedToUnconsolidatedRealEstateFundMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_CarriedInterestRelatedToUnconsolidatedRealEstateFundMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Information pertaining to carried interest related to Unconsolidated Real Estate Fund.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_CarriedInterestRelatedToUnconsolidatedRealEstateFundMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carried Interest Related To Unconsolidated Real Estate Fund [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_CarriedInterestRelatedToUnconsolidatedRealEstateFundMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carried interest</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_RelatedPartyOtherThanThoseSpecifiedMember" xlink:label="bhm_RelatedPartyOtherThanThoseSpecifiedMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_RelatedPartyOtherThanThoseSpecifiedMember" xlink:to="bhm_RelatedPartyOtherThanThoseSpecifiedMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_RelatedPartyOtherThanThoseSpecifiedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Information pertaining to party or parties related to reporting entity that are other than those specified in other disclosures. Includes, but is not limited to, affiliate, entity for which investment is accounted for by equity method, trust for benefit of employees, and principal owner, management, and members of immediate family.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_RelatedPartyOtherThanThoseSpecifiedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related Party, Other Than Those Specified [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_RelatedPartyOtherThanThoseSpecifiedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related party, other</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_CapitalImprovementCostReimbursementsMember" xlink:label="bhm_CapitalImprovementCostReimbursementsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_CapitalImprovementCostReimbursementsMember" xlink:to="bhm_CapitalImprovementCostReimbursementsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_CapitalImprovementCostReimbursementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information relating to the capital improvement costs reimbursements as per the agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_CapitalImprovementCostReimbursementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capital Improvement Cost Reimbursements [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_CapitalImprovementCostReimbursementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capital improvement cost reimbursements</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SecurityDeposit" xlink:label="us-gaap_SecurityDeposit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SecurityDeposit" xlink:to="us-gaap_SecurityDeposit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SecurityDeposit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Security deposit</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_JointVentureAgreementMember" xlink:label="bhm_JointVentureAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_JointVentureAgreementMember" xlink:to="bhm_JointVentureAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_JointVentureAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Information pertaining to joint venture agreement with Harmony.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_JointVentureAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Joint Venture Agreement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_JointVentureAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Joint venture agreement with Harmony</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_FacilitationFeePayableToAffiliateForConsultingServices" xlink:label="bhm_FacilitationFeePayableToAffiliateForConsultingServices" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_FacilitationFeePayableToAffiliateForConsultingServices" xlink:to="bhm_FacilitationFeePayableToAffiliateForConsultingServices_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_FacilitationFeePayableToAffiliateForConsultingServices_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of facilitation or consulting fee payable by a joint venture partner to an affiliate of the manager in connection with services related to a real estate development project.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_FacilitationFeePayableToAffiliateForConsultingServices_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Facilitation Fee Payable to Affiliate for Consulting Services</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_FacilitationFeePayableToAffiliateForConsultingServices_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Facilitation or consulting fee payable</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_EntityStockSalesAgreementMember" xlink:label="bhm_EntityStockSalesAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_EntityStockSalesAgreementMember" xlink:to="bhm_EntityStockSalesAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_EntityStockSalesAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Information pertaining to agreement regarding sale of the entity's stock.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_EntityStockSalesAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Entity Stock Sales Agreement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_EntityStockSalesAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock offering agreement</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_SellingCommissionsAndDiscountsMember" xlink:label="bhm_SellingCommissionsAndDiscountsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_SellingCommissionsAndDiscountsMember" xlink:to="bhm_SellingCommissionsAndDiscountsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_SellingCommissionsAndDiscountsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Information pertaining to selling commissions and discounts.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_SellingCommissionsAndDiscountsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Selling Commissions And Discounts [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_SellingCommissionsAndDiscountsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Selling commissions and discounts</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_DealerManagerFeesAndDiscountsMember" xlink:label="bhm_DealerManagerFeesAndDiscountsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_DealerManagerFeesAndDiscountsMember" xlink:to="bhm_DealerManagerFeesAndDiscountsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_DealerManagerFeesAndDiscountsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Information pertaining to selling commissions and discounts.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_DealerManagerFeesAndDiscountsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Dealer Manager Fees And Discounts [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_DealerManagerFeesAndDiscountsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Dealer manager fees</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsidiarySaleOfStockAxis" xlink:label="us-gaap_SubsidiarySaleOfStockAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsidiarySaleOfStockAxis" xlink:to="us-gaap_SubsidiarySaleOfStockAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsidiarySaleOfStockAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Stock [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SaleOfStockNameOfTransactionDomain" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SaleOfStockNameOfTransactionDomain" xlink:to="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Stock [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PrivatePlacementMember" xlink:label="us-gaap_PrivatePlacementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PrivatePlacementMember" xlink:to="us-gaap_PrivatePlacementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PrivatePlacementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Private Placement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PrivatePlacementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">DST Program</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_SellingCommissionsAndDealerManagerFeesAsPercentageOfGrossOfferingProceeds" xlink:label="bhm_SellingCommissionsAndDealerManagerFeesAsPercentageOfGrossOfferingProceeds" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_SellingCommissionsAndDealerManagerFeesAsPercentageOfGrossOfferingProceeds" xlink:to="bhm_SellingCommissionsAndDealerManagerFeesAsPercentageOfGrossOfferingProceeds_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_SellingCommissionsAndDealerManagerFeesAsPercentageOfGrossOfferingProceeds_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the selling commissions and dealer manager fees as percentage of gross offering proceeds.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_SellingCommissionsAndDealerManagerFeesAsPercentageOfGrossOfferingProceeds_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Selling Commissions and Dealer Manager Fees as Percentage of Gross Offering Proceeds</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_SellingCommissionsAndDealerManagerFeesAsPercentageOfGrossOfferingProceeds_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Selling commissions and dealer manager fees as percentage of gross offering proceeds</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_SellingCommissionsAndDiscountsIncurred" xlink:label="bhm_SellingCommissionsAndDiscountsIncurred" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_SellingCommissionsAndDiscountsIncurred" xlink:to="bhm_SellingCommissionsAndDiscountsIncurred_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_SellingCommissionsAndDiscountsIncurred_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the selling commissions and discounts incurred.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_SellingCommissionsAndDiscountsIncurred_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Selling Commissions And Discounts Incurred</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_SellingCommissionsAndDiscountsIncurred_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Selling commissions and discounts incurred</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_DealerManagerFeesAndDiscounts" xlink:label="bhm_DealerManagerFeesAndDiscounts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_DealerManagerFeesAndDiscounts" xlink:to="bhm_DealerManagerFeesAndDiscounts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_DealerManagerFeesAndDiscounts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the dealer manager fees and discounts.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_DealerManagerFeesAndDiscounts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Dealer Manager Fees And Discounts</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_DealerManagerFeesAndDiscounts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Dealer manager fees and discounts</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_AmountReimbursedForOfferingCosts" xlink:label="bhm_AmountReimbursedForOfferingCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_AmountReimbursedForOfferingCosts" xlink:to="bhm_AmountReimbursedForOfferingCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_AmountReimbursedForOfferingCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the amount reimbursed for offering costs.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_AmountReimbursedForOfferingCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount Reimbursed for Offering Costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_AmountReimbursedForOfferingCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount reimbursed for offering costs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SeriesAPreferredStockMember" xlink:label="us-gaap_SeriesAPreferredStockMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SeriesAPreferredStockMember" xlink:to="us-gaap_SeriesAPreferredStockMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SeriesAPreferredStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Series A Preferred Stock [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SeriesAPreferredStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Series A Preferred Stock</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SeriesBPreferredStockMember" xlink:label="us-gaap_SeriesBPreferredStockMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SeriesBPreferredStockMember" xlink:to="us-gaap_SeriesBPreferredStockMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SeriesBPreferredStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Series B Preferred Stock [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SeriesBPreferredStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Series B Preferred Stock</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:to="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Antidilutive Securities [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AntidilutiveSecuritiesNameDomain" xlink:label="us-gaap_AntidilutiveSecuritiesNameDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AntidilutiveSecuritiesNameDomain" xlink:to="us-gaap_AntidilutiveSecuritiesNameDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AntidilutiveSecuritiesNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Antidilutive Securities, Name [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedStockMember" xlink:label="us-gaap_RestrictedStockMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RestrictedStockMember" xlink:to="us-gaap_RestrictedStockMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RestrictedStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Restricted Stock [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RestrictedStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Restricted Stock Grants</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_RestrictedStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Restricted Stock</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConvertiblePreferredStockMember" xlink:label="us-gaap_ConvertiblePreferredStockMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConvertiblePreferredStockMember" xlink:to="us-gaap_ConvertiblePreferredStockMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConvertiblePreferredStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Preferred Stock [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConvertiblePreferredStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Convertible Preferred Stock</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_CommonStockDividendRatio" xlink:label="bhm_CommonStockDividendRatio" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_CommonStockDividendRatio" xlink:to="bhm_CommonStockDividendRatio_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_CommonStockDividendRatio_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the ratio at which classes of common stock participate in dividends. A ratio of 1 means that specified classes participate equally.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_CommonStockDividendRatio_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Dividend Ratio</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_CommonStockDividendRatio_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Dividend ratio</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityDividendsAdjustment" xlink:label="us-gaap_TemporaryEquityDividendsAdjustment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquityDividendsAdjustment" xlink:to="us-gaap_TemporaryEquityDividendsAdjustment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TemporaryEquityDividendsAdjustment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Dividends, Adjustment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_TemporaryEquityDividendsAdjustment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Less preferred stock dividends</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment" xlink:label="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment" xlink:to="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Accretion to Redemption Value, Adjustment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Less preferred stock accretion</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred stock accretion</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedStockAwardForfeituresDividends" xlink:label="us-gaap_RestrictedStockAwardForfeituresDividends" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RestrictedStockAwardForfeituresDividends" xlink:to="us-gaap_RestrictedStockAwardForfeituresDividends_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RestrictedStockAwardForfeituresDividends_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Restricted Stock Award, Forfeitures, Dividends</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_RestrictedStockAwardForfeituresDividends_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Less dividends on restricted stock and LTIP Units expected to vest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLossFromDiscontinuedOperationsAvailableToCommonShareholdersBasic" xlink:label="us-gaap_NetIncomeLossFromDiscontinuedOperationsAvailableToCommonShareholdersBasic" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetIncomeLossFromDiscontinuedOperationsAvailableToCommonShareholdersBasic" xlink:to="us-gaap_NetIncomeLossFromDiscontinuedOperationsAvailableToCommonShareholdersBasic_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetIncomeLossFromDiscontinuedOperationsAvailableToCommonShareholdersBasic_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Income (Loss) from Discontinued Operations Available to Common Shareholders, Basic</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetIncomeLossFromDiscontinuedOperationsAvailableToCommonShareholdersBasic_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net loss attributable to common stockholders</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:to="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Antidilutive Securities Excluded from Computation of Earnings Per Share, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares excluded from the diluted shares calculations</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_PartnersCapitalAccountUnitToShareExchangesRatio" xlink:label="bhm_PartnersCapitalAccountUnitToShareExchangesRatio" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_PartnersCapitalAccountUnitToShareExchangesRatio" xlink:to="bhm_PartnersCapitalAccountUnitToShareExchangesRatio_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_PartnersCapitalAccountUnitToShareExchangesRatio_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ratio of shares obtained in exchange for ownership units.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_PartnersCapitalAccountUnitToShareExchangesRatio_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Partners' Capital Account, Unit To Share Exchanges Ratio</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_PartnersCapitalAccountUnitToShareExchangesRatio_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ratio of exchange between ownership units and common stock</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_RedeemablePreferredStockMaximumOfferingAmount" xlink:label="bhm_RedeemablePreferredStockMaximumOfferingAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_RedeemablePreferredStockMaximumOfferingAmount" xlink:to="bhm_RedeemablePreferredStockMaximumOfferingAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_RedeemablePreferredStockMaximumOfferingAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The maximum offering amount of temporary equity.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_RedeemablePreferredStockMaximumOfferingAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redeemable Preferred Stock, Maximum Offering Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_RedeemablePreferredStockMaximumOfferingAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum offering amount</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_TemporaryEquitySharesIssuedIncludingRedeemedShares" xlink:label="bhm_TemporaryEquitySharesIssuedIncludingRedeemedShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_TemporaryEquitySharesIssuedIncludingRedeemedShares" xlink:to="bhm_TemporaryEquitySharesIssuedIncludingRedeemedShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_TemporaryEquitySharesIssuedIncludingRedeemedShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares issued during the period which includes shares redeemed.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_TemporaryEquitySharesIssuedIncludingRedeemedShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Shares Issued Including Redeemed Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_TemporaryEquitySharesIssuedIncludingRedeemedShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Aggregate shares issued to date (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock" xlink:label="us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock" xlink:to="us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Issuance of Preferred Stock and Preference Stock</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net proceeds of approximately</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockRedeemedOrCalledDuringPeriodShares" xlink:label="us-gaap_StockRedeemedOrCalledDuringPeriodShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockRedeemedOrCalledDuringPeriodShares" xlink:to="us-gaap_StockRedeemedOrCalledDuringPeriodShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockRedeemedOrCalledDuringPeriodShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Redeemed or Called During Period, Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockRedeemedOrCalledDuringPeriodShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Series A Preferred Stock redeemed (in shares)</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_StockRedeemedOrCalledDuringPeriodInCashShares" xlink:label="bhm_StockRedeemedOrCalledDuringPeriodInCashShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_StockRedeemedOrCalledDuringPeriodInCashShares" xlink:to="bhm_StockRedeemedOrCalledDuringPeriodInCashShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_StockRedeemedOrCalledDuringPeriodInCashShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of stock bought back by the entity at the exercise price or redemption price in cash.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_StockRedeemedOrCalledDuringPeriodInCashShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Redeemed or Called During Period In Cash, Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_StockRedeemedOrCalledDuringPeriodInCashShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Series A Preferred Stock redeemed in cash (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StockRepurchaseProgramAuthorizedAmount1" xlink:label="srt_StockRepurchaseProgramAuthorizedAmount1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_StockRepurchaseProgramAuthorizedAmount1" xlink:to="srt_StockRepurchaseProgramAuthorizedAmount1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_StockRepurchaseProgramAuthorizedAmount1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Repurchase Program Authorized Dollar Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_StockRepurchaseProgramAuthorizedAmount1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock repurchase plan, authorized amount</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockRepurchaseProgramPeriodInForce1" xlink:label="us-gaap_StockRepurchaseProgramPeriodInForce1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockRepurchaseProgramPeriodInForce1" xlink:to="us-gaap_StockRepurchaseProgramPeriodInForce1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockRepurchaseProgramPeriodInForce1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share Repurchase Program, Period in Force</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockRepurchaseProgramPeriodInForce1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock repurchase plan, period in force</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockRepurchasedDuringPeriodShares" xlink:label="us-gaap_StockRepurchasedDuringPeriodShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockRepurchasedDuringPeriodShares" xlink:to="us-gaap_StockRepurchasedDuringPeriodShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockRepurchasedDuringPeriodShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Repurchased During Period, Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockRepurchasedDuringPeriodShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repurchase of Class A common stock</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_OpAndLtipUnitHoldersMember" xlink:label="bhm_OpAndLtipUnitHoldersMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_OpAndLtipUnitHoldersMember" xlink:to="bhm_OpAndLtipUnitHoldersMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_OpAndLtipUnitHoldersMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">OP And LTIP Unit holders [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_OpAndLtipUnitHoldersMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">OP And LTIP Unit holders</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_OpUnitHoldersMember" xlink:label="bhm_OpUnitHoldersMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_OpUnitHoldersMember" xlink:to="bhm_OpUnitHoldersMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_OpUnitHoldersMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">OP Unit holders [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_OpUnitHoldersMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">OP Unit holders</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_LtipUnitHoldersMember" xlink:label="bhm_LtipUnitHoldersMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_LtipUnitHoldersMember" xlink:to="bhm_LtipUnitHoldersMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_LtipUnitHoldersMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">LTIP Unit holders [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_LtipUnitHoldersMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">LTIP Unit holders</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_CLongTermIncentivePlanUnitsMember" xlink:label="bhm_CLongTermIncentivePlanUnitsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_CLongTermIncentivePlanUnitsMember" xlink:to="bhm_CLongTermIncentivePlanUnitsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_CLongTermIncentivePlanUnitsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to C-LTIP units.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_CLongTermIncentivePlanUnitsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">C Long Term Incentive Plan Units [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_CLongTermIncentivePlanUnitsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">C-LTIP Units</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PartnersCapitalAccountUnits" xlink:label="us-gaap_PartnersCapitalAccountUnits" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PartnersCapitalAccountUnits" xlink:to="us-gaap_PartnersCapitalAccountUnits_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PartnersCapitalAccountUnits_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Partners' Capital Account, Units</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesIssuedForServices" xlink:label="us-gaap_StockIssuedDuringPeriodSharesIssuedForServices" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodSharesIssuedForServices" xlink:to="us-gaap_StockIssuedDuringPeriodSharesIssuedForServices_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodSharesIssuedForServices_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Issued for Services</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodSharesIssuedForServices_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of awards granted for base management fee</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockGrantedDuringPeriodValueSharebasedCompensation" xlink:label="us-gaap_StockGrantedDuringPeriodValueSharebasedCompensation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockGrantedDuringPeriodValueSharebasedCompensation" xlink:to="us-gaap_StockGrantedDuringPeriodValueSharebasedCompensation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockGrantedDuringPeriodValueSharebasedCompensation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares Granted, Value, Share-Based Payment Arrangement, after Forfeiture</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockGrantedDuringPeriodValueSharebasedCompensation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Value of awards granted for base management fee</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PlanNameAxis" xlink:label="us-gaap_PlanNameAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PlanNameAxis" xlink:to="us-gaap_PlanNameAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PlanNameAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Plan Name [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PlanNameDomain" xlink:label="us-gaap_PlanNameDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PlanNameDomain" xlink:to="us-gaap_PlanNameDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PlanNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Plan Name [Domain]</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_BhmIncentivePlansMember" xlink:label="bhm_BhmIncentivePlansMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_BhmIncentivePlansMember" xlink:to="bhm_BhmIncentivePlansMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_BhmIncentivePlansMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to BHM Incentive Plans.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_BhmIncentivePlansMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BHM Incentive Plans [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_BhmIncentivePlansMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BHM Incentive Plans</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_PeakJvFourMember" xlink:label="bhm_PeakJvFourMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_PeakJvFourMember" xlink:to="bhm_PeakJvFourMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_PeakJvFourMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to Peak JV 4 includes the portfolios formerly presented as Savannah 319.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_PeakJvFourMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Peak JV Four</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bhm_PeakJvFourMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Savannah-84, formerly Peak JV 4</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsGranted" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsGranted" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsGranted" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsGranted_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsGranted_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Non-Option Equity Instruments, Granted</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsGranted_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of units granted</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AllocatedShareBasedCompensationExpense" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AllocatedShareBasedCompensationExpense" xlink:to="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Allocated Share-based Compensation Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Expense recognized</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:to="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Employee Service Share-based Compensation, Nonvested Awards, Compensation Cost Not yet Recognized</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unrecognized compensation</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:to="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Employee Service Share-based Compensation, Nonvested Awards, Compensation Cost Not yet Recognized, Period for Recognition</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Remaining compensation cost is expected to be recognized (in years)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DividendsPayableTable" xlink:label="us-gaap_DividendsPayableTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DividendsPayableTable" xlink:to="us-gaap_DividendsPayableTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DividendsPayableTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Dividends Payable [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DividendsAxis" xlink:label="us-gaap_DividendsAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DividendsAxis" xlink:to="us-gaap_DividendsAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DividendsAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Dividends [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DividendsDomain" xlink:label="us-gaap_DividendsDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DividendsDomain" xlink:to="us-gaap_DividendsDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DividendsDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Dividends [Domain]</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_O2025Q14DividendsMember" xlink:label="bhm_O2025Q14DividendsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_O2025Q14DividendsMember" xlink:to="bhm_O2025Q14DividendsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_O2025Q14DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">O 2025 Q1 fourth Dividends.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_O2025Q14DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">O 2025 Q1 4 Dividends [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_O2025Q14DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">O 2025 Q1 fourth Dividends</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_O2026Q11DividendsMember" xlink:label="bhm_O2026Q11DividendsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_O2026Q11DividendsMember" xlink:to="bhm_O2026Q11DividendsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_O2026Q11DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">O 2026 Q1 first Dividends.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_O2026Q11DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">O 2026 Q1 1 Dividends [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_O2026Q11DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">O 2026 Q1 1 Dividends</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_O2026Q12DividendsMember" xlink:label="bhm_O2026Q12DividendsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_O2026Q12DividendsMember" xlink:to="bhm_O2026Q12DividendsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_O2026Q12DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">O 2026 Q1 second Dividends.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_O2026Q12DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">O 2026 Q1 2 Dividends [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_O2026Q12DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">O 2026 Q1 2 Dividends</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_O2026Q13DividendsMember" xlink:label="bhm_O2026Q13DividendsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_O2026Q13DividendsMember" xlink:to="bhm_O2026Q13DividendsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_O2026Q13DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">O 2026 Q1 third dividends.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_O2026Q13DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">O 2026 Q1 3 Dividends [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_O2026Q13DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">O 2026 Q1 3 Dividends</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_S2025Q43DividendsMember" xlink:label="bhm_S2025Q43DividendsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_S2025Q43DividendsMember" xlink:to="bhm_S2025Q43DividendsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_S2025Q43DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to special dividend of third month of fourth quarter of year 2025.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_S2025Q43DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">S 2025 Q4 3 Dividends [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_S2025Q43DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">S 2025 Q4 Third Dividends</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_S2026M1DividendsMember" xlink:label="bhm_S2026M1DividendsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_S2026M1DividendsMember" xlink:to="bhm_S2026M1DividendsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_S2026M1DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to special dividend paid/payable for the month of January 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_S2026M1DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">S 2026 M1 Dividends [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_S2026M1DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">S 2026 M1 Dividends</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_S2026M2DividendsMember" xlink:label="bhm_S2026M2DividendsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_S2026M2DividendsMember" xlink:to="bhm_S2026M2DividendsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_S2026M2DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to special dividend paid/payable for the month of February 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_S2026M2DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">S 2026 M2 Dividends [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_S2026M2DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">S 2026 M2 Dividends</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_S2026M3DividendsMember" xlink:label="bhm_S2026M3DividendsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_S2026M3DividendsMember" xlink:to="bhm_S2026M3DividendsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_S2026M3DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to special dividend paid/payable for the month of March 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_S2026M3DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">S 2026 M3 Dividends [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_S2026M3DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">S 2026 M3 Dividends</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_O2026M1DividendsMember" xlink:label="bhm_O2026M1DividendsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_O2026M1DividendsMember" xlink:to="bhm_O2026M1DividendsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_O2026M1DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to ordinary dividend paid/payable for the month of January 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_O2026M1DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">O 2026 M1 Dividends [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_O2026M1DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">O 2026 M1 Dividends</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_O2026M2DividendsMember" xlink:label="bhm_O2026M2DividendsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_O2026M2DividendsMember" xlink:to="bhm_O2026M2DividendsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_O2026M2DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to ordinary dividend paid/payable for the month of February 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_O2026M2DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">O 2026 M2 Dividends [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_O2026M2DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">O 2026 M2 Dividends</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_O2026M3DividendsMember" xlink:label="bhm_O2026M3DividendsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_O2026M3DividendsMember" xlink:to="bhm_O2026M3DividendsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_O2026M3DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to ordinary dividend paid/payable for the month of March 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_O2026M3DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">O 2026 M3 Dividends [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_O2026M3DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">O 2026 M3 Dividends</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DividendsPayableLineItems" xlink:label="us-gaap_DividendsPayableLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DividendsPayableLineItems" xlink:to="us-gaap_DividendsPayableLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DividendsPayableLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Dividends Payable [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DividendsPayableLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stockholders' Equity and Redeemable Preferred Stock</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DividendsPayableDateDeclaredDayMonthAndYear" xlink:label="us-gaap_DividendsPayableDateDeclaredDayMonthAndYear" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DividendsPayableDateDeclaredDayMonthAndYear" xlink:to="us-gaap_DividendsPayableDateDeclaredDayMonthAndYear_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DividendsPayableDateDeclaredDayMonthAndYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Dividends Payable, Date Declared</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DividendsPayableDateDeclaredDayMonthAndYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Declaration Date</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DividendsPayableDateOfRecordDayMonthAndYear" xlink:label="us-gaap_DividendsPayableDateOfRecordDayMonthAndYear" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DividendsPayableDateOfRecordDayMonthAndYear" xlink:to="us-gaap_DividendsPayableDateOfRecordDayMonthAndYear_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DividendsPayableDateOfRecordDayMonthAndYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Dividends Payable, Date of Record</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DividendsPayableDateOfRecordDayMonthAndYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Record Date</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockDividendsPerShareDeclared" xlink:label="us-gaap_CommonStockDividendsPerShareDeclared" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockDividendsPerShareDeclared" xlink:to="us-gaap_CommonStockDividendsPerShareDeclared_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockDividendsPerShareDeclared_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Dividends, Per Share, Declared</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockDividendsPerShareDeclared_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock dividends declared (in dollars per share)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockDividendsPerShareDeclared" xlink:label="us-gaap_PreferredStockDividendsPerShareDeclared" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockDividendsPerShareDeclared" xlink:to="us-gaap_PreferredStockDividendsPerShareDeclared_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PreferredStockDividendsPerShareDeclared_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Stock, Dividends Per Share, Declared</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_PreferredStockDividendsPerShareDeclared_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred stock dividends declared (in dollars per share)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DividendPayableDateToBePaidDayMonthAndYear" xlink:label="us-gaap_DividendPayableDateToBePaidDayMonthAndYear" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DividendPayableDateToBePaidDayMonthAndYear" xlink:to="us-gaap_DividendPayableDateToBePaidDayMonthAndYear_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DividendPayableDateToBePaidDayMonthAndYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Dividends Payable, Date to be Paid</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DividendPayableDateToBePaidDayMonthAndYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Date Paid</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DividendPayableDateToBePaidDayMonthAndYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Paid / Payable Date</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_PreferredStockAverageTermOfSofrConsideredForDeterminationOfEnhancedSpecialDividend" xlink:label="bhm_PreferredStockAverageTermOfSofrConsideredForDeterminationOfEnhancedSpecialDividend" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_PreferredStockAverageTermOfSofrConsideredForDeterminationOfEnhancedSpecialDividend" xlink:to="bhm_PreferredStockAverageTermOfSofrConsideredForDeterminationOfEnhancedSpecialDividend_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_PreferredStockAverageTermOfSofrConsideredForDeterminationOfEnhancedSpecialDividend_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Average Term of SOFR considered for determination of enhanced special dividends on preferred stock.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_PreferredStockAverageTermOfSofrConsideredForDeterminationOfEnhancedSpecialDividend_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Stock Average Term Of SOFR Considered For Determination Of Enhanced Special Dividend</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_PreferredStockAverageTermOfSofrConsideredForDeterminationOfEnhancedSpecialDividend_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Average of the Term SOFR</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_PreferredStockDenominatorPercentageConsideredForDeterminationOfEnhancedSpecialDividends" xlink:label="bhm_PreferredStockDenominatorPercentageConsideredForDeterminationOfEnhancedSpecialDividends" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_PreferredStockDenominatorPercentageConsideredForDeterminationOfEnhancedSpecialDividends" xlink:to="bhm_PreferredStockDenominatorPercentageConsideredForDeterminationOfEnhancedSpecialDividends_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_PreferredStockDenominatorPercentageConsideredForDeterminationOfEnhancedSpecialDividends_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The percentage considered for determination of enhanced special dividends on preferred stock.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_PreferredStockDenominatorPercentageConsideredForDeterminationOfEnhancedSpecialDividends_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Stock Denominator Percentage Considered For Determination Of Enhanced Special Dividends</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_PreferredStockDenominatorPercentageConsideredForDeterminationOfEnhancedSpecialDividends_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage consideration for determination of enhanced special dividends</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_TemporaryEquitySpecialDividendBasisSpreadOnVariableRatePercent" xlink:label="bhm_TemporaryEquitySpecialDividendBasisSpreadOnVariableRatePercent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_TemporaryEquitySpecialDividendBasisSpreadOnVariableRatePercent" xlink:to="bhm_TemporaryEquitySpecialDividendBasisSpreadOnVariableRatePercent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_TemporaryEquitySpecialDividendBasisSpreadOnVariableRatePercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The basis spread on variable rate used to calculate special dividend payments on shares of temporary equity.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_TemporaryEquitySpecialDividendBasisSpreadOnVariableRatePercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Special Dividend, Basis Spread On Variable Rate, Percent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_TemporaryEquitySpecialDividendBasisSpreadOnVariableRatePercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Special dividend, spread on variable rate (as a percent)</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_TemporaryEquitySpecialDividendEffectiveRatePercent" xlink:label="bhm_TemporaryEquitySpecialDividendEffectiveRatePercent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_TemporaryEquitySpecialDividendEffectiveRatePercent" xlink:to="bhm_TemporaryEquitySpecialDividendEffectiveRatePercent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_TemporaryEquitySpecialDividendEffectiveRatePercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The percentage rate used to calculate special dividend payments on shares of temporary equity.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_TemporaryEquitySpecialDividendEffectiveRatePercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Special Dividend Effective Rate, Percent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_TemporaryEquitySpecialDividendEffectiveRatePercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Special dividend target rate (as a percent)</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_DividendRateToWhichSpecialDividendIsAddedInDollarsPerShare" xlink:label="bhm_DividendRateToWhichSpecialDividendIsAddedInDollarsPerShare" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_DividendRateToWhichSpecialDividendIsAddedInDollarsPerShare" xlink:to="bhm_DividendRateToWhichSpecialDividendIsAddedInDollarsPerShare_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_DividendRateToWhichSpecialDividendIsAddedInDollarsPerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Dividend rate to which special dividend is added</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_DividendRateToWhichSpecialDividendIsAddedInDollarsPerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Dividend Rate To Which Special Dividend Is Added (in dollars per share)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_DividendRateToWhichSpecialDividendIsAddedInDollarsPerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Dividend rate to which special dividend is added (in dollars per share)</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_OperatingPartnershipUnitsMember" xlink:label="bhm_OperatingPartnershipUnitsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_OperatingPartnershipUnitsMember" xlink:to="bhm_OperatingPartnershipUnitsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_OperatingPartnershipUnitsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Partnership Units One [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_OperatingPartnershipUnitsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">OP Units</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_LongTermIncentivePlanUnitsAndCLongTermIncentivePlanUnitsMember" xlink:label="bhm_LongTermIncentivePlanUnitsAndCLongTermIncentivePlanUnitsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_LongTermIncentivePlanUnitsAndCLongTermIncentivePlanUnitsMember" xlink:to="bhm_LongTermIncentivePlanUnitsAndCLongTermIncentivePlanUnitsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_LongTermIncentivePlanUnitsAndCLongTermIncentivePlanUnitsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">This member represents the information about the long-term incentive plan units and c-long-term incentive plan units.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_LongTermIncentivePlanUnitsAndCLongTermIncentivePlanUnitsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Incentive Plan Units And C-Long-Term Incentive Plan Units[Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_LongTermIncentivePlanUnitsAndCLongTermIncentivePlanUnitsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">LTIP / C-LTIP Units</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Dividends" xlink:label="us-gaap_Dividends" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Dividends" xlink:to="us-gaap_Dividends_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Dividends_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Dividends</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_Dividends_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Distributions Declared</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfDividends" xlink:label="us-gaap_PaymentsOfDividends" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsOfDividends" xlink:to="us-gaap_PaymentsOfDividends_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsOfDividends_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments of Dividends</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PaymentsOfDividends_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total Distribution</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_PaymentsOfDividends_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Dividends paid</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherCommitmentsTable" xlink:label="us-gaap_OtherCommitmentsTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherCommitmentsTable" xlink:to="us-gaap_OtherCommitmentsTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherCommitmentsTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Commitments [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherCommitmentsLineItems" xlink:label="us-gaap_OtherCommitmentsLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherCommitmentsLineItems" xlink:to="us-gaap_OtherCommitmentsLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherCommitmentsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Commitments [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherCommitmentsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commitments and Contingencies</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractualObligation" xlink:label="us-gaap_ContractualObligation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ContractualObligation" xlink:to="us-gaap_ContractualObligation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ContractualObligation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contractual Obligation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ContractualObligation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contractual commitments</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_NumberOfConsolidatedUnitsUnderConstruction" xlink:label="bhm_NumberOfConsolidatedUnitsUnderConstruction" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_NumberOfConsolidatedUnitsUnderConstruction" xlink:to="bhm_NumberOfConsolidatedUnitsUnderConstruction_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_NumberOfConsolidatedUnitsUnderConstruction_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The number of consolidated units under construction.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_NumberOfConsolidatedUnitsUnderConstruction_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of Consolidated Units Under Construction</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_NumberOfConsolidatedUnitsUnderConstruction_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of investment units under construction</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_RemainingEstimatedProjectCosts" xlink:label="bhm_RemainingEstimatedProjectCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_RemainingEstimatedProjectCosts" xlink:to="bhm_RemainingEstimatedProjectCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_RemainingEstimatedProjectCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of remaining estimated cost of the project.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_RemainingEstimatedProjectCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Remaining Estimated Project Costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_RemainingEstimatedProjectCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Remaining estimated project costs</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_OperatingPropertiesNumberOfUnitsToBeAcquired" xlink:label="bhm_OperatingPropertiesNumberOfUnitsToBeAcquired" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_OperatingPropertiesNumberOfUnitsToBeAcquired" xlink:to="bhm_OperatingPropertiesNumberOfUnitsToBeAcquired_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_OperatingPropertiesNumberOfUnitsToBeAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">It represent the operating properties number of units to be acquired.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_OperatingPropertiesNumberOfUnitsToBeAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Properties Number Of Units To Be Acquired</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_OperatingPropertiesNumberOfUnitsToBeAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of units acquired</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_OperatingPropertiesRemainingNumberOfUnitsToBeAcquired" xlink:label="bhm_OperatingPropertiesRemainingNumberOfUnitsToBeAcquired" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_OperatingPropertiesRemainingNumberOfUnitsToBeAcquired" xlink:to="bhm_OperatingPropertiesRemainingNumberOfUnitsToBeAcquired_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_OperatingPropertiesRemainingNumberOfUnitsToBeAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">It represents the remaining operating properties number of units to be acquired.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_OperatingPropertiesRemainingNumberOfUnitsToBeAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Properties Remaining Number Of Units To Be Acquired</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_OperatingPropertiesRemainingNumberOfUnitsToBeAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of remaining units acquired</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseCost" xlink:label="us-gaap_OperatingLeaseCost" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseCost" xlink:to="us-gaap_OperatingLeaseCost_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseCost_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Lease, Cost</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseCost_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net rent expense of lease</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseRightOfUseAsset" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseRightOfUseAsset" xlink:to="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Lease, Right-of-Use Asset</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Right-of-use asset</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiability" xlink:label="us-gaap_OperatingLeaseLiability" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseLiability" xlink:to="us-gaap_OperatingLeaseLiability_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Lease, Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lease liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total operating lease liability</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseDiscountRate" xlink:label="us-gaap_LesseeOperatingLeaseDiscountRate" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseDiscountRate" xlink:to="us-gaap_LesseeOperatingLeaseDiscountRate_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseDiscountRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Discount Rate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeOperatingLeaseDiscountRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Discount rate of lease (as a percent)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseRemainingLeaseTerm" xlink:label="us-gaap_LesseeOperatingLeaseRemainingLeaseTerm" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseRemainingLeaseTerm" xlink:to="us-gaap_LesseeOperatingLeaseRemainingLeaseTerm_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseRemainingLeaseTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Remaining Lease Term</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeOperatingLeaseRemainingLeaseTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Remaining lease term (in years)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract" xlink:label="us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract" xlink:to="us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, to be Paid, Fiscal Year Maturity [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Future minimum lease payments and total operating lease liability</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, to be Paid, Remainder of Fiscal Year</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2026 (April 1 - December 31)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, to be Paid, Year One</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, to be Paid, Year Two</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2028</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, to be Paid, Year Three</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2029</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, to be Paid, Year Four</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2030</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:label="bhm_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:to="bhm_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of lessee's undiscounted obligation for lease payment for operating lease due after fourth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, to be Paid, after Year Four</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Thereafter</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, to be Paid</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total future minimum lease payments (undiscounted cash flows)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, Undiscounted Excess Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Difference between future undiscounted cash flows and discounted cash flows</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable" xlink:label="us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable" xlink:to="us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reconciliation of Assets from Segment to Consolidated [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingAssetReconcilingItemLineItems" xlink:label="us-gaap_SegmentReportingAssetReconcilingItemLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SegmentReportingAssetReconcilingItemLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Segment Reporting, Asset Reconciling Item [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SegmentReportingAssetReconcilingItemLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Segment Information</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfReportableSegments" xlink:label="us-gaap_NumberOfReportableSegments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NumberOfReportableSegments" xlink:to="us-gaap_NumberOfReportableSegments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of Reportable Segments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of reportable segments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidationItemsAxis" xlink:label="srt_ConsolidationItemsAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ConsolidationItemsAxis" xlink:to="srt_ConsolidationItemsAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ConsolidationItemsAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consolidation Items [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidationItemsDomain" xlink:label="srt_ConsolidationItemsDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ConsolidationItemsDomain" xlink:to="srt_ConsolidationItemsDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingSegmentsMember" xlink:label="us-gaap_OperatingSegmentsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingSegmentsMember" xlink:to="us-gaap_OperatingSegmentsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingSegmentsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Segments [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingSegmentsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Segments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MaterialReconcilingItemsMember" xlink:label="us-gaap_MaterialReconcilingItemsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MaterialReconcilingItemsMember" xlink:to="us-gaap_MaterialReconcilingItemsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MaterialReconcilingItemsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Segment Reporting, Reconciling Item, Excluding Corporate Non segment [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MaterialReconcilingItemsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reconciling Items</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingIncomeLoss" xlink:label="us-gaap_OperatingIncomeLoss" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingIncomeLoss" xlink:to="us-gaap_OperatingIncomeLoss_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Income (Loss)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total net operating income</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_InterestIncomeDebtSecuritiesAvailableForSaleNonOperating" xlink:label="bhm_InterestIncomeDebtSecuritiesAvailableForSaleNonOperating" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_InterestIncomeDebtSecuritiesAvailableForSaleNonOperating" xlink:to="bhm_InterestIncomeDebtSecuritiesAvailableForSaleNonOperating_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_InterestIncomeDebtSecuritiesAvailableForSaleNonOperating_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of interest income, amortization of premium and accretion of discount on investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale); classified as non operating.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_InterestIncomeDebtSecuritiesAvailableForSaleNonOperating_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Income, Debt Securities, Available For Sale, Non Operating</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_InterestIncomeDebtSecuritiesAvailableForSaleNonOperating_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income from preferred equity investments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestIncomeOther" xlink:label="us-gaap_InterestIncomeOther" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestIncomeOther" xlink:to="us-gaap_InterestIncomeOther_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InterestIncomeOther_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Income, Other</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InterestIncomeOther_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest income</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_O2026Q21DividendsMember" xlink:label="bhm_O2026Q21DividendsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_O2026Q21DividendsMember" xlink:to="bhm_O2026Q21DividendsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_O2026Q21DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to ordinary dividend paid/payable for the month of April 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_O2026Q21DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">O 2026 Q2 1 Dividends [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_O2026Q21DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">O 2026 Q2 1 Dividends</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_O2026Q22DividendsMember" xlink:label="bhm_O2026Q22DividendsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_O2026Q22DividendsMember" xlink:to="bhm_O2026Q22DividendsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_O2026Q22DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to ordinary dividend paid/payable for the month of May 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_O2026Q22DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">O 2026 Q2 2 Dividends [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bhm_O2026Q22DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">O 2026 Q2 2 Dividends</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_O2026Q23DividendsMember" xlink:label="bhm_O2026Q23DividendsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_O2026Q23DividendsMember" xlink:to="bhm_O2026Q23DividendsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_O2026Q23DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to ordinary dividend paid/payable for the month of June 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_O2026Q23DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">O 2026 Q2 3 Dividends [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_O2026Q23DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">O 2026 Q2 3 Dividends</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_S2026Q21DividendsMember" xlink:label="bhm_S2026Q21DividendsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_S2026Q21DividendsMember" xlink:to="bhm_S2026Q21DividendsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_S2026Q21DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to special dividend paid/payable for the month of April 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_S2026Q21DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">S 2026 Q2 1 Dividends [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_S2026Q21DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">S 2026 Q2 1 Dividends</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_S2026Q22DividendsMember" xlink:label="bhm_S2026Q22DividendsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_S2026Q22DividendsMember" xlink:to="bhm_S2026Q22DividendsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_S2026Q22DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to special dividend paid/payable for the month of May 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_S2026Q22DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">S 2026 Q2 2 Dividends [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_S2026Q22DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">S 2026 Q2 2 Dividends</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_S2026Q23DividendsMember" xlink:label="bhm_S2026Q23DividendsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_S2026Q23DividendsMember" xlink:to="bhm_S2026Q23DividendsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_S2026Q23DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to special dividend paid/payable for the month of June 2026.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_S2026Q23DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">S 2026 Q2 3 Dividends [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_S2026Q23DividendsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">S 2026 Q2 3 Dividends</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_PreferredStockDenominatorConsideredForDeterminationOfSpecialDailyDividends" xlink:label="bhm_PreferredStockDenominatorConsideredForDeterminationOfSpecialDailyDividends" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_PreferredStockDenominatorConsideredForDeterminationOfSpecialDailyDividends" xlink:to="bhm_PreferredStockDenominatorConsideredForDeterminationOfSpecialDailyDividends_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_PreferredStockDenominatorConsideredForDeterminationOfSpecialDailyDividends_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Denominator considered for determination of special daily dividends on preferred stock.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_PreferredStockDenominatorConsideredForDeterminationOfSpecialDailyDividends_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Stock, Denominator Considered For Determination Of Special Daily Dividends</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_PreferredStockDenominatorConsideredForDeterminationOfSpecialDailyDividends_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Series A preferred stock denominator considered for determination of special daily dividends</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockDividendsPerShareCashPaid" xlink:label="us-gaap_PreferredStockDividendsPerShareCashPaid" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockDividendsPerShareCashPaid" xlink:to="us-gaap_PreferredStockDividendsPerShareCashPaid_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PreferredStockDividendsPerShareCashPaid_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Stock, Dividends, Per Share, Cash Paid</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PreferredStockDividendsPerShareCashPaid_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Distribution per Share</label>
    <loc xlink:type="locator" xlink:href="bhm-20260331.xsd#bhm_RealEstateNumberOfUnitsAdditionalAcquired" xlink:label="bhm_RealEstateNumberOfUnitsAdditionalAcquired" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bhm_RealEstateNumberOfUnitsAdditionalAcquired" xlink:to="bhm_RealEstateNumberOfUnitsAdditionalAcquired_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bhm_RealEstateNumberOfUnitsAdditionalAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of units acquired additional under build to rent development projects at the end of the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bhm_RealEstateNumberOfUnitsAdditionalAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Real Estate, Number Of Units Additional Acquired</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bhm_RealEstateNumberOfUnitsAdditionalAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of units acquired additional</label>
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