<?xml version="1.0" encoding="US-ASCII"?>
<!-- DFIN New ActiveDisclosure (SM) XBRL Schema Document - http://www.dfinsolutions.com/ -->
<!-- Creation Date :2025-04-25T14:22:26.6302+00:00 -->
<!-- Copyright (c) 2025 Donnelley Financial Solutions, Inc. All Rights Reserved. -->
<xsd:schema targetNamespace="http://www.ghiinvestors.com/20250425" attributeFormDefault="unqualified" elementFormDefault="qualified" xmlns:dtr-types="http://www.xbrl.org/dtr/type/2024-01-31" xmlns:enum2="http://xbrl.org/2020/extensible-enumerations-2.0" xmlns:ecd-sub="http://xbrl.sec.gov/ecd-sub/2024" xmlns:ecd="http://xbrl.sec.gov/ecd/2024" xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:us-gaap="http://fasb.org/us-gaap/2024" xmlns:dei="http://xbrl.sec.gov/dei/2024" xmlns:ghi="http://www.ghiinvestors.com/20250425" xmlns:xbrldt="http://xbrl.org/2005/xbrldt" xmlns:xbrli="http://www.xbrl.org/2003/instance" xmlns:xlink="http://www.w3.org/1999/xlink">
  <xsd:import schemaLocation="http://www.xbrl.org/2003/xbrl-instance-2003-12-31.xsd" namespace="http://www.xbrl.org/2003/instance"/>
  <xsd:import schemaLocation="http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd" namespace="http://www.xbrl.org/2003/linkbase"/>
  <xsd:import schemaLocation="http://www.xbrl.org/2005/xbrldt-2005.xsd" namespace="http://xbrl.org/2005/xbrldt"/>
  <xsd:import schemaLocation="https://xbrl.sec.gov/ecd/2024/ecd-sub-2024.xsd" namespace="http://xbrl.sec.gov/ecd-sub/2024"/>
  <xsd:import schemaLocation="https://xbrl.sec.gov/dei/2024/dei-2024.xsd" namespace="http://xbrl.sec.gov/dei/2024"/>
  <xsd:import schemaLocation="https://www.xbrl.org/dtr/type/2024-01-31/types.xsd" namespace="http://www.xbrl.org/dtr/type/2024-01-31"/>
  <xsd:import schemaLocation="https://xbrl.fasb.org/us-gaap/2024/elts/us-gaap-2024.xsd" namespace="http://fasb.org/us-gaap/2024"/>
  <xsd:import schemaLocation="https://xbrl.sec.gov/ecd/2024/ecd-2024.xsd" namespace="http://xbrl.sec.gov/ecd/2024"/>
  <xsd:annotation>
    <xsd:appinfo>
      <link:roleType roleURI="http://www.ghiinvestors.com/20250425/taxonomy/role/DocumentDocumentAndEntityInformation" id="DocumentDocumentAndEntityInformation">
        <link:definition>100000 - Document - Document and Entity Information</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:linkbase id="lnk">
        <link:roleRef roleURI="http://www.ghiinvestors.com/20250425/taxonomy/role/DocumentDocumentAndEntityInformation" xlink:href="ghi-20250425.xsd#DocumentDocumentAndEntityInformation" xlink:type="simple"/>
        <link:labelLink xlink:role="http://www.xbrl.org/2003/role/link" xlink:title="labelLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityCentralIndexKey" xlink:label="dei_EntityCentralIndexKey"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_CoverAbstract" xlink:label="dei_CoverAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_AmendmentFlag" xlink:label="dei_AmendmentFlag"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_DocumentType" xlink:label="dei_DocumentType"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityRegistrantName" xlink:label="dei_EntityRegistrantName"/>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Central Index Key</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Central Index Key</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CoverAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cover [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AmendmentFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amendment Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentType_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityRegistrantName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Registrant Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityRegistrantName_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Registrant Name</link:label>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityCentralIndexKey" xlink:to="dei_EntityCentralIndexKey_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_CoverAbstract" xlink:to="dei_CoverAbstract_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_AmendmentFlag" xlink:to="dei_AmendmentFlag_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_DocumentType" xlink:to="dei_DocumentType_lbl"/>
          <link:labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityRegistrantName" xlink:to="dei_EntityRegistrantName_lbl"/>
        </link:labelLink>
        <link:presentationLink xlink:role="http://www.ghiinvestors.com/20250425/taxonomy/role/DocumentDocumentAndEntityInformation" xlink:title="presentationLink" xlink:type="extended">
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_CoverAbstract" xlink:label="dei_CoverAbstract"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_DocumentType" xlink:label="dei_DocumentType"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_AmendmentFlag" xlink:label="dei_AmendmentFlag"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityRegistrantName" xlink:label="dei_EntityRegistrantName"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2024/dei-2024.xsd#dei_EntityCentralIndexKey" xlink:label="dei_EntityCentralIndexKey"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_DocumentType" order="49.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_AmendmentFlag" order="50.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_EntityRegistrantName" order="51.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
          <link:presentationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="dei_CoverAbstract" xlink:to="dei_EntityCentralIndexKey" order="52.0" priority="2" use="optional" preferredLabel="http://www.xbrl.org/2003/role/label"/>
        </link:presentationLink>
      </link:linkbase>
    </xsd:appinfo>
  </xsd:annotation>
</xsd:schema>
