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

<!--XBRL Document Created with Wdesk from Workiva-->
<!--Copyright 2022 Workiva-->
<!--r:852cce9f-4ea6-4897-a485-2a2e1d5d38a0,g:8cdef3c3-43f2-4c39-b00c-38a983addf7f-->
<xs:schema xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:codi="http://www.compasstrust.com/20220712" xmlns:xbrli="http://www.xbrl.org/2003/instance" xmlns:dtr-types="http://www.xbrl.org/dtr/type/2020-01-21" attributeFormDefault="unqualified" elementFormDefault="qualified" targetNamespace="http://www.compasstrust.com/20220712">
  <xs:import namespace="http://fasb.org/us-gaap/2021-01-31" schemaLocation="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd"/>
  <xs:import namespace="http://www.w3.org/1999/xlink" schemaLocation="http://www.xbrl.org/2003/xlink-2003-12-31.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/2020-01-21" schemaLocation="https://www.xbrl.org/dtr/type/2020-01-21/types.xsd"/>
  <xs:import namespace="http://xbrl.sec.gov/dei/2021q4" schemaLocation="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.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="codi-20220712_lab.xml" xlink:role="http://www.xbrl.org/2003/role/labelLinkbaseRef" 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="codi-20220712_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="codi-20220712_def.xml" xlink:role="http://www.xbrl.org/2003/role/definitionLinkbaseRef" xlink:type="simple"/>
      <link:roleType id="CoverDocument" roleURI="http://www.compasstrust.com/role/CoverDocument">
        <link:definition>0001001 - Document - Cover Document</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="StatementofFinancialPosition" roleURI="http://www.compasstrust.com/role/StatementofFinancialPosition">
        <link:definition>1001002 - Statement - Statement of Financial Position</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="StatementofIncome" roleURI="http://www.compasstrust.com/role/StatementofIncome">
        <link:definition>1002003 - Statement - Statement of Income</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="StatementofCashFlows" roleURI="http://www.compasstrust.com/role/StatementofCashFlows">
        <link:definition>1003004 - Statement - Statement of Cash Flows</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
    </xs:appinfo>
  </xs:annotation>
  <xs:element id="codi_SeriesAPreferredSharesRepresentingSeriesATrustPreferredInterestInCompassDiversifiedHoldingsMember" abstract="true" name="SeriesAPreferredSharesRepresentingSeriesATrustPreferredInterestInCompassDiversifiedHoldingsMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="codi_SeriesBPreferredSharesRepresentingSeriesBTrustPreferredInterestInCompassDiversifiedHoldingsMember" abstract="true" name="SeriesBPreferredSharesRepresentingSeriesBTrustPreferredInterestInCompassDiversifiedHoldingsMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="codi_SeriesCPreferredSharesRepresentingSeriesCTrustPreferredInterestInCompassDiversifiedHoldingsMemberDomain" abstract="true" name="SeriesCPreferredSharesRepresentingSeriesCTrustPreferredInterestInCompassDiversifiedHoldingsMemberDomain" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="codi_SharesRepresentingBeneficialInterestsInCompassDiversifiedHoldingsMember" abstract="true" name="SharesRepresentingBeneficialInterestsInCompassDiversifiedHoldingsMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
</xs:schema>
