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<!-- Generated by DFIN XBRL Schema Document - http://www.dfinsolutions.com/ - on 25-06-2026 05:52:42 PM -->
<!-- Copyright(c) 2026 Donnelley Financial Solutions, Inc. All Rights Reserved. -->
<schema targetNamespace="http://www.blackrock.com/20260622" xmlns="http://www.w3.org/2001/XMLSchema" xmlns:bfiii="http://www.blackrock.com/20260622" xmlns:dei="http://xbrl.sec.gov/dei/2025" xmlns:srt-types="http://fasb.org/srt-types/2025" xmlns:deprecated="http://www.xbrl.org/2009/role/deprecated" xmlns:dtr="http://www.xbrl.org/2009/dtr" xmlns:oef="http://xbrl.sec.gov/oef/2025" xmlns:ref="http://www.xbrl.org/2006/ref" xmlns:xbrldt="http://xbrl.org/2005/xbrldt" xmlns:xl="http://www.xbrl.org/2003/XLink" xmlns:us-gaap="http://fasb.org/us-gaap/2025" xmlns:oef-pre="http://xbrl.sec.gov/oef-pre/2025" xmlns:oef-lab="http://xbrl.sec.gov/oef-lab/2025" xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:country="http://xbrl.sec.gov/country/2025" xmlns:us-roles="http://fasb.org/us-roles/2025" xmlns:enum2="http://xbrl.org/2020/extensible-enumerations-2.0" xmlns:us-types="http://fasb.org/us-types/2025" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:dtr-types="http://www.xbrl.org/dtr/type/2024-01-31" xmlns:oef-def="http://xbrl.sec.gov/oef-def/2025" xmlns:negated="http://www.xbrl.org/2009/role/negated" xmlns:xbrldi="http://xbrl.org/2006/xbrldi" xmlns:srt="http://fasb.org/srt/2025" xmlns:oef-sr="http://xbrl.sec.gov/oef-sr/2025" xmlns:srt-roles="http://fasb.org/srt-roles/2025" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xbrli="http://www.xbrl.org/2003/instance" xmlns:stpr="http://xbrl.sec.gov/stpr/2025" elementFormDefault="qualified">
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	<import namespace="http://www.xbrl.org/2003/linkbase" schemaLocation="http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd"/>
	<import namespace="http://xbrl.sec.gov/dei/2025" schemaLocation="https://xbrl.sec.gov/dei/2025/dei-2025.xsd"/>
	<import namespace="http://fasb.org/us-types/2025" schemaLocation="https://xbrl.fasb.org/us-gaap/2025/elts/us-types-2025.xsd"/>
	<import namespace="http://www.xbrl.org/dtr/type/2024-01-31" schemaLocation="https://www.xbrl.org/dtr/type/2024-01-31/types.xsd"/>   
	<import namespace="http://xbrl.sec.gov/country/2025" schemaLocation="https://xbrl.sec.gov/country/2025/country-2025.xsd"/>
	<import namespace="http://fasb.org/srt/2025" schemaLocation="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd"/>
	<import namespace="http://fasb.org/srt-types/2025" schemaLocation="https://xbrl.fasb.org/srt/2025/elts/srt-types-2025.xsd"/>
	<import namespace="http://xbrl.sec.gov/oef-sr/2025" schemaLocation="https://xbrl.sec.gov/oef/2025/oef-sr-2025.xsd"/>
	<import namespace="http://fasb.org/us-gaap/2025" schemaLocation="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd"/>
	<import namespace="http://fasb.org/us-roles/2025" schemaLocation="https://xbrl.fasb.org/us-gaap/2025/elts/us-roles-2025.xsd"/>
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				<link:roleRef roleURI="http://xbrl.sec.gov/oef/role/ShareholderReportHoldingsDetails" xlink:type="simple" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#ShareholderReportHoldingsDetails"/>
				<link:roleRef roleURI="http://xbrl.sec.gov/oef/role/ShareholderReportLineGraphDetails" xlink:type="simple" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#ShareholderReportLineGraphDetails"/>
				<link:roleRef roleURI="http://xbrl.sec.gov/oef/role/ShareholderReportAverageAnnualReturnDetails" xlink:type="simple" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#ShareholderReportAverageAnnualReturnDetails"/>
				<link:roleRef roleURI="http://xbrl.sec.gov/oef/role/ClassOnly" xlink:type="simple" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#ClassOnly"/>
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				<link:roleRef roleURI="http://xbrl.sec.gov/oef/role/LargestHoldingOnly" xlink:type="simple" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#LargestHoldingOnly"/>
				<link:roleRef roleURI="http://xbrl.sec.gov/oef/role/Other1CategoryOnly" xlink:type="simple" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#Other1CategoryOnly"/>
				<link:roleRef roleURI="http://xbrl.sec.gov/oef/role/AdditionalIndexOnly" xlink:type="simple" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#AdditionalIndexOnly"/>
				<link:roleRef roleURI="http://xbrl.sec.gov/oef/role/BroadBasedIndexOnly" xlink:type="simple" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#BroadBasedIndexOnly"/>
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					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="ShareClassDomain" xlink:to="C000220944Member" order="15.0"/>
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					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="ShareClassDomain" xlink:to="C000220947Member" order="17.0"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_C000220949Member" xlink:label="C000220949Member"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="ShareClassDomain" xlink:to="C000220949Member" order="18.0"/>
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					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="ShareClassDomain" xlink:to="C000220952Member" order="19.0"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_C000220950Member" xlink:label="C000220950Member"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="ShareClassDomain" xlink:to="C000220950Member" order="20.0"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_C000220951Member" xlink:label="C000220951Member"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="ShareClassDomain" xlink:to="C000220951Member" order="21.0"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_C000220955Member" xlink:label="C000220955Member"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="ShareClassDomain" xlink:to="C000220955Member" order="22.0"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_C000220953Member" xlink:label="C000220953Member"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="ShareClassDomain" xlink:to="C000220953Member" order="23.0"/>
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					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="ShareClassDomain" xlink:to="C000220954Member" order="24.0"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_C000220957Member" xlink:label="C000220957Member"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="ShareClassDomain" xlink:to="C000220957Member" order="25.0"/>
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					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="ShareClassDomain" xlink:to="C000220958Member" order="26.0"/>
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					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="ShareClassDomain" xlink:to="C000220956Member" order="27.0"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_C000244506Member" xlink:label="C000244506Member"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="ShareClassDomain" xlink:to="C000244506Member" order="28.0"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_C000244507Member" xlink:label="C000244507Member"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="ShareClassDomain" xlink:to="C000244507Member" order="29.0"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_C000251819Member" xlink:label="C000251819Member"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="ShareClassDomain" xlink:to="C000251819Member" order="30.0"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_C000251818Member" xlink:label="C000251818Member"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="ShareClassDomain" xlink:to="C000251818Member" order="31.0"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_C000251817Member" xlink:label="C000251817Member"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="ShareClassDomain" xlink:to="C000251817Member" order="32.0"/>
				</link:definitionLink>
				<link:definitionLink xlink:type="extended" xlink:role="http://xbrl.sec.gov/oef/role/Other1CategoryOnly">               
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_OtherCategory1Domain" xlink:label="OtherCategory1Domain"/>
				</link:definitionLink>
				<link:definitionLink xlink:type="extended" xlink:role="http://xbrl.sec.gov/oef/role/Other2CategoryOnly">               
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_OtherCategory2Domain" xlink:label="OtherCategory2Domain"/>
				</link:definitionLink>
				<link:definitionLink xlink:type="extended" xlink:role="http://xbrl.sec.gov/oef/role/LargestHoldingOnly">               
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_LargestHoldingsDomain" xlink:label="LargestHoldingsDomain"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_ISharesMSCIEmergingMarketsSmallCapETFMember" xlink:label="ISharesMSCIEmergingMarketsSmallCapETFMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="LargestHoldingsDomain" xlink:to="ISharesMSCIEmergingMarketsSmallCapETFMember" order="1.0"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_ISharesMSCICanadaETFMember" xlink:label="ISharesMSCICanadaETFMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="LargestHoldingsDomain" xlink:to="ISharesMSCICanadaETFMember" order="2.0"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_ISharesMSCIEAFESmallCapETFMember" xlink:label="ISharesMSCIEAFESmallCapETFMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="LargestHoldingsDomain" xlink:to="ISharesMSCIEAFESmallCapETFMember" order="3.0"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_ISharesDevelopedRealEstateIndexFundClassKMember" xlink:label="ISharesDevelopedRealEstateIndexFundClassKMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="LargestHoldingsDomain" xlink:to="ISharesDevelopedRealEstateIndexFundClassKMember" order="4.0"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_ISharesESGAwareMSCIUSASmallCapETFMember" xlink:label="ISharesESGAwareMSCIUSASmallCapETFMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="LargestHoldingsDomain" xlink:to="ISharesESGAwareMSCIUSASmallCapETFMember" order="5.0"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_ISharesESGAwareMSCIEMETFMember" xlink:label="ISharesESGAwareMSCIEMETFMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="LargestHoldingsDomain" xlink:to="ISharesESGAwareMSCIEMETFMember" order="6.0"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_ISharesTIPSBondETFMember" xlink:label="ISharesTIPSBondETFMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="LargestHoldingsDomain" xlink:to="ISharesTIPSBondETFMember" order="7.0"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_ISharesESGAwareMSCIEAFEETFMember" xlink:label="ISharesESGAwareMSCIEAFEETFMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="LargestHoldingsDomain" xlink:to="ISharesESGAwareMSCIEAFEETFMember" order="8.0"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_ISharesESGAwareMSCIUSAETFMember" xlink:label="ISharesESGAwareMSCIUSAETFMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="LargestHoldingsDomain" xlink:to="ISharesESGAwareMSCIUSAETFMember" order="9.0"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_ISharesESGAwareUSAggregateBondETFMember" xlink:label="ISharesESGAwareUSAggregateBondETFMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="LargestHoldingsDomain" xlink:to="ISharesESGAwareUSAggregateBondETFMember" order="10.0"/>
				</link:definitionLink>
				<link:definitionLink xlink:type="extended" xlink:role="http://xbrl.sec.gov/oef/role/SalesLoadOnly">
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_WithSalesLoadMember" xlink:label="WithSalesLoadMember"/>
				</link:definitionLink>
				<link:definitionLink xlink:type="extended" xlink:role="http://fasb.org/us-gaap/role/eedm/ExtensibleEnumerationLists">               
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeCategorizationMember" xlink:label="InvestmentTypeCategorizationMember"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_EquityFundsSecuritiesMember" xlink:label="EquityFundsSecuritiesMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="InvestmentTypeCategorizationMember" xlink:to="EquityFundsSecuritiesMember" order="1.0"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FixedIncomeFundsMember" xlink:label="FixedIncomeFundsMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="InvestmentTypeCategorizationMember" xlink:to="FixedIncomeFundsMember" order="2.0"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MoneyMarketFundsMember" xlink:label="MoneyMarketFundsMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="InvestmentTypeCategorizationMember" xlink:to="MoneyMarketFundsMember" order="3.0"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_LiabilitiesInExcessOfOtherAssetsMember" xlink:label="LiabilitiesInExcessOfOtherAssetsMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="InvestmentTypeCategorizationMember" xlink:to="LiabilitiesInExcessOfOtherAssetsMember" order="4.0"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MunicipalBondsMember" xlink:label="MunicipalBondsMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="InvestmentTypeCategorizationMember" xlink:to="MunicipalBondsMember" order="5.0"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherInvestmentsMember" xlink:label="OtherInvestmentsMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="InvestmentTypeCategorizationMember" xlink:to="OtherInvestmentsMember" order="6.0"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_USGovernmentSponsoredAgencySecuritiesMember" xlink:label="USGovernmentSponsoredAgencySecuritiesMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="InvestmentTypeCategorizationMember" xlink:to="USGovernmentSponsoredAgencySecuritiesMember" order="7.0"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_USTreasuryObligationsMember" xlink:label="USTreasuryObligationsMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="InvestmentTypeCategorizationMember" xlink:to="USTreasuryObligationsMember" order="8.0"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_NonAgencyMortgageBackedSecuritiesMember" xlink:label="NonAgencyMortgageBackedSecuritiesMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="InvestmentTypeCategorizationMember" xlink:to="NonAgencyMortgageBackedSecuritiesMember" order="9.0"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_ForeignAgencyObligationsMember" xlink:label="ForeignAgencyObligationsMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="InvestmentTypeCategorizationMember" xlink:to="ForeignAgencyObligationsMember" order="10.0"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_CapitalTrustsMember" xlink:label="CapitalTrustsMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="InvestmentTypeCategorizationMember" xlink:to="CapitalTrustsMember" order="11.0"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_InvestmentCompaniesMember" xlink:label="InvestmentCompaniesMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="InvestmentTypeCategorizationMember" xlink:to="InvestmentCompaniesMember" order="12.0"/>
				</link:definitionLink>
				<link:definitionLink xlink:type="extended" xlink:role="http://xbrl.sec.gov/oef/role/BroadBasedIndexOnly">               
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_BroadBasedIndexDomain" xlink:label="BroadBasedIndexDomain"/>
				</link:definitionLink>
				<link:definitionLink xlink:type="extended" xlink:role="http://xbrl.sec.gov/oef/role/AdditionalIndexOnly">              
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_AdditionalIndexDomain" xlink:label="AdditionalIndexDomain"/>
				</link:definitionLink>
				<link:definitionLink xlink:type="extended" xlink:role="http://xbrl.sec.gov/oef/role/MaturityOnly">
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_MaturityDomain" xlink:label="MaturityDomain"/>
				</link:definitionLink>
				<link:definitionLink xlink:type="extended" xlink:role="http://xbrl.sec.gov/oef/role/IndustrySectorOnly">
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_IndustrySectorDomain" xlink:label="IndustrySectorDomain"/>
				</link:definitionLink>
				<link:definitionLink xlink:type="extended" xlink:role="http://xbrl.sec.gov/oef/role/CreditQualityOnly">
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_CreditQualityDomain" xlink:label="CreditQualityDomain"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_NRMember" xlink:label="NRMember"/>
					<link:definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:from="CreditQualityDomain" xlink:to="NRMember" order="1.0"/>
				</link:definitionLink>
				<!--GeographicRegionOnly use only for STPR-->
				<link:definitionLink xlink:type="extended" xlink:role="http://xbrl.sec.gov/oef/role/GeographicRegionOnly">
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/oef/2025/oef-2025.xsd#oef_GeographicRegionDomain" xlink:label="GeographicRegionDomain"/>
				</link:definitionLink>
				<link:labelLink xlink:type="extended" xlink:role="http://www.xbrl.org/2003/role/link">               
					<link:loc xlink:type="locator" xlink:href="#bfiii_C000220929Member" xlink:label="C000220929Member"/>
					<link:label xlink:type="resource" xlink:label="label_C000220929Member" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">C000220929 [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="C000220929Member" xlink:to="label_C000220929Member"/>
										<link:label xlink:type="resource" xlink:label="label_C000220929Member_2" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xml:lang="en-US">Class K</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="C000220929Member" xlink:to="label_C000220929Member_2"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_C000220931Member" xlink:label="C000220931Member"/>
					<link:label xlink:type="resource" xlink:label="label_C000220931Member" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">C000220931 [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="C000220931Member" xlink:to="label_C000220931Member"/>
										<link:label xlink:type="resource" xlink:label="label_C000220931Member_2" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xml:lang="en-US">Investor A</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="C000220931Member" xlink:to="label_C000220931Member_2"/>
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					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="StandardPoorsARatingMember" xlink:to="label_StandardPoorsARatingMember"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StandardPoorsBBBRatingMember" xlink:label="StandardPoorsBBBRatingMember"/>
					<link:label xlink:type="resource" xlink:label="label_StandardPoorsBBBRatingMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Standard &amp; Poor&apos;s, BBB Rating [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="StandardPoorsBBBRatingMember" xlink:to="label_StandardPoorsBBBRatingMember"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StandardPoorsBBRatingMember" xlink:label="StandardPoorsBBRatingMember"/>
					<link:label xlink:type="resource" xlink:label="label_StandardPoorsBBRatingMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Standard &amp; Poor&apos;s, BB Rating [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="StandardPoorsBBRatingMember" xlink:to="label_StandardPoorsBBRatingMember"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StandardPoorsBRatingMember" xlink:label="StandardPoorsBRatingMember"/>
					<link:label xlink:type="resource" xlink:label="label_StandardPoorsBRatingMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Standard &amp; Poor&apos;s, B Rating [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="StandardPoorsBRatingMember" xlink:to="label_StandardPoorsBRatingMember"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StandardPoorsCCCRatingMember" xlink:label="StandardPoorsCCCRatingMember"/>
					<link:label xlink:type="resource" xlink:label="label_StandardPoorsCCCRatingMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Standard &amp; Poor&apos;s, CCC Rating [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="StandardPoorsCCCRatingMember" xlink:to="label_StandardPoorsCCCRatingMember"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StandardPoorsCCRatingMember" xlink:label="StandardPoorsCCRatingMember"/>
					<link:label xlink:type="resource" xlink:label="label_StandardPoorsCCRatingMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Standard &amp; Poor&apos;s, CC Rating [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="StandardPoorsCCRatingMember" xlink:to="label_StandardPoorsCCRatingMember"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StandardPoorsCRatingMember" xlink:label="StandardPoorsCRatingMember"/>
					<link:label xlink:type="resource" xlink:label="label_StandardPoorsCRatingMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Standard &amp; Poor&apos;s, C Rating [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="StandardPoorsCRatingMember" xlink:to="label_StandardPoorsCRatingMember"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StandardPoorsDRatingMember" xlink:label="StandardPoorsDRatingMember"/>
					<link:label xlink:type="resource" xlink:label="label_StandardPoorsDRatingMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Standard &amp; Poor&apos;s, D Rating [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="StandardPoorsDRatingMember" xlink:to="label_StandardPoorsDRatingMember"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CorporateBondSecuritiesMember" xlink:label="CorporateBondSecuritiesMember"/>
					<link:label xlink:type="resource" xlink:label="label_CorporateBondSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Corporate Bond Securities [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="CorporateBondSecuritiesMember" xlink:to="label_CorporateBondSecuritiesMember"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MunicipalBondsMember" xlink:label="MunicipalBondsMember"/>
					<link:label xlink:type="resource" xlink:label="label_MunicipalBondsMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Municipal Bonds [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="MunicipalBondsMember" xlink:to="label_MunicipalBondsMember"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockMember" xlink:label="CommonStockMember"/>
					<link:label xlink:type="resource" xlink:label="label_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Common Stock [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="CommonStockMember" xlink:to="label_CommonStockMember"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetBackedSecuritiesMember" xlink:label="AssetBackedSecuritiesMember"/>
					<link:label xlink:type="resource" xlink:label="label_AssetBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Asset-Backed Securities [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="AssetBackedSecuritiesMember" xlink:to="label_AssetBackedSecuritiesMember"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherInvestmentsMember" xlink:label="OtherInvestmentsMember"/>
					<link:label xlink:type="resource" xlink:label="label_OtherInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Other Investments [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="OtherInvestmentsMember" xlink:to="label_OtherInvestmentsMember"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_C000244506Member" xlink:label="C000244506Member"/>
					<link:label xlink:type="resource" xlink:label="label_C000244506Member" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">C000244506 [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="C000244506Member" xlink:to="label_C000244506Member"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_C000244507Member" xlink:label="C000244507Member"/>
					<link:label xlink:type="resource" xlink:label="label_C000244507Member" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">C000244507 [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="C000244507Member" xlink:to="label_C000244507Member"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_USGovernmentSponsoredAgencySecuritiesMember" xlink:label="USGovernmentSponsoredAgencySecuritiesMember"/>
					<link:label xlink:type="resource" xlink:label="label_USGovernmentSponsoredAgencySecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">U S Government Sponsored Agency Securities [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="USGovernmentSponsoredAgencySecuritiesMember" xlink:to="label_USGovernmentSponsoredAgencySecuritiesMember"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_USTreasuryObligationsMember" xlink:label="USTreasuryObligationsMember"/>
					<link:label xlink:type="resource" xlink:label="label_USTreasuryObligationsMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">U S Treasury Obligations [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="USTreasuryObligationsMember" xlink:to="label_USTreasuryObligationsMember"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_NonAgencyMortgageBackedSecuritiesMember" xlink:label="NonAgencyMortgageBackedSecuritiesMember"/>
					<link:label xlink:type="resource" xlink:label="label_NonAgencyMortgageBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Non Agency Mortgage Backed Securities [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="NonAgencyMortgageBackedSecuritiesMember" xlink:to="label_NonAgencyMortgageBackedSecuritiesMember"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_ForeignAgencyObligationsMember" xlink:label="ForeignAgencyObligationsMember"/>
					<link:label xlink:type="resource" xlink:label="label_ForeignAgencyObligationsMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Foreign Agency Obligations [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ForeignAgencyObligationsMember" xlink:to="label_ForeignAgencyObligationsMember"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_CapitalTrustsMember" xlink:label="CapitalTrustsMember"/>
					<link:label xlink:type="resource" xlink:label="label_CapitalTrustsMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Capital Trusts [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="CapitalTrustsMember" xlink:to="label_CapitalTrustsMember"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_InvestmentCompaniesMember" xlink:label="InvestmentCompaniesMember"/>
					<link:label xlink:type="resource" xlink:label="label_InvestmentCompaniesMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Investment Companies [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="InvestmentCompaniesMember" xlink:to="label_InvestmentCompaniesMember"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_NRMember" xlink:label="NRMember"/>
					<link:label xlink:type="resource" xlink:label="label_NRMember" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">N R [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="NRMember" xlink:to="label_NRMember"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_C000251819Member" xlink:label="C000251819Member"/>
					<link:label xlink:type="resource" xlink:label="label_C000251819Member" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">C000251819 [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="C000251819Member" xlink:to="label_C000251819Member"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_C000251818Member" xlink:label="C000251818Member"/>
					<link:label xlink:type="resource" xlink:label="label_C000251818Member" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">C000251818 [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="C000251818Member" xlink:to="label_C000251818Member"/>
					<link:loc xlink:type="locator" xlink:href="#bfiii_C000251817Member" xlink:label="C000251817Member"/>
					<link:label xlink:type="resource" xlink:label="label_C000251817Member" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">C000251817 [Member]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="C000251817Member" xlink:to="label_C000251817Member"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeAxis" xlink:label="InvestmentTypeAxis"/>
					<link:label xlink:type="resource" xlink:label="label_InvestmentTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Investment Type [Axis]</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="InvestmentTypeAxis" xlink:to="label_InvestmentTypeAxis" priority="1"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsNet" xlink:label="AssetsNet"/>
					<link:label xlink:type="resource" xlink:label="label_AssetsNet" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Net Assets</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="AssetsNet" xlink:to="label_AssetsNet" priority="1"/>
					<link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentCompanyPortfolioTurnover" xlink:label="InvestmentCompanyPortfolioTurnover"/>
					<link:label xlink:type="resource" xlink:label="label_InvestmentCompanyPortfolioTurnover" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">Investment Company Portfolio Turnover</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="InvestmentCompanyPortfolioTurnover" xlink:to="label_InvestmentCompanyPortfolioTurnover" priority="1"/>                
					<link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_NoTradingSymbolFlag" xlink:label="dei_NoTradingSymbolFlag"/>
					<link:label xlink:type="resource" xlink:label="label_NoTradingSymbolFlag" xlink:role="http://www.xbrl.org/2003/role/label" xml:lang="en-US">No Trading Symbol Flag</link:label>
					<link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_NoTradingSymbolFlag" xlink:to="label_NoTradingSymbolFlag" priority="1"/>		
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	<element name="ISharesMSCIEAFESmallCapETFMember" id="bfiii_ISharesMSCIEAFESmallCapETFMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
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	<element name="EquityFundsSecuritiesMember" id="bfiii_EquityFundsSecuritiesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
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	<element name="C000220955Member" id="bfiii_C000220955Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="C000220953Member" id="bfiii_C000220953Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="C000220954Member" id="bfiii_C000220954Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="C000220957Member" id="bfiii_C000220957Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="C000220958Member" id="bfiii_C000220958Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="C000220956Member" id="bfiii_C000220956Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="C000244506Member" id="bfiii_C000244506Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="C000244507Member" id="bfiii_C000244507Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="USGovernmentSponsoredAgencySecuritiesMember" id="bfiii_USGovernmentSponsoredAgencySecuritiesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="USTreasuryObligationsMember" id="bfiii_USTreasuryObligationsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="NonAgencyMortgageBackedSecuritiesMember" id="bfiii_NonAgencyMortgageBackedSecuritiesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="ForeignAgencyObligationsMember" id="bfiii_ForeignAgencyObligationsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="CapitalTrustsMember" id="bfiii_CapitalTrustsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="InvestmentCompaniesMember" id="bfiii_InvestmentCompaniesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="NRMember" id="bfiii_NRMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="C000251819Member" id="bfiii_C000251819Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="C000251818Member" id="bfiii_C000251818Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
	<element name="C000251817Member" id="bfiii_C000251817Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" abstract="true" nillable="true" xbrli:periodType="duration"/>
</schema>
