<?xml version="1.0" encoding="UTF-8"?>

<!--XBRL Document Created with the Workiva Platform-->
<!--Copyright 2026 Workiva-->
<!--r:019ddf67-09b2-7cf9-847d-b38bc9310eee,g:98e08e82-b24d-49b6-805a-520157de724e-->
<xs:schema xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:ck0001737924="http://www.churchillam.com/20260610" xmlns:xbrli="http://www.xbrl.org/2003/instance" xmlns:dtr-types="http://www.xbrl.org/dtr/type/2024-01-31" attributeFormDefault="unqualified" elementFormDefault="qualified" targetNamespace="http://www.churchillam.com/20260610">
  <xs:import namespace="http://fasb.org/us-gaap/2025" schemaLocation="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd"/>
  <xs:import namespace="http://www.xbrl.org/2003/instance" schemaLocation="http://www.xbrl.org/2003/xbrl-instance-2003-12-31.xsd"/>
  <xs:import namespace="http://www.xbrl.org/2003/linkbase" schemaLocation="http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd"/>
  <xs:import namespace="http://www.xbrl.org/dtr/type/2024-01-31" schemaLocation="https://www.xbrl.org/dtr/type/2024-01-31/types.xsd"/>
  <xs:import namespace="http://xbrl.org/2006/xbrldi" schemaLocation="http://www.xbrl.org/2006/xbrldi-2006.xsd"/>
  <xs:import namespace="http://xbrl.sec.gov/cef-pre/2025" schemaLocation="https://xbrl.sec.gov/cef/2025/cef-2025_pre.xsd"/>
  <xs:import namespace="http://xbrl.sec.gov/dei/2025" schemaLocation="https://xbrl.sec.gov/dei/2025/dei-2025.xsd"/>
  <xs:annotation>
    <xs:appinfo>
      <link:linkbaseRef xmlns:xlink="http://www.w3.org/1999/xlink" xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="ck0001737924-20260610_pre.xml" xlink:role="http://www.xbrl.org/2003/role/presentationLinkbaseRef" xlink:type="simple"/>
      <link:linkbaseRef xmlns:xlink="http://www.w3.org/1999/xlink" xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="ck0001737924-20260610_def.xml" xlink:role="http://www.xbrl.org/2003/role/definitionLinkbaseRef" xlink:type="simple"/>
      <link:linkbaseRef xmlns:xlink="http://www.w3.org/1999/xlink" xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="ck0001737924-20260610_lab.xml" xlink:role="http://www.xbrl.org/2003/role/labelLinkbaseRef" xlink:type="simple"/>
    </xs:appinfo>
  </xs:annotation>
  <xs:element id="ck0001737924_SubscriptionRightsMember" abstract="true" name="SubscriptionRightsMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
</xs:schema>
