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Variable Interest Entities - Variable Interest Entities Property Asset Carrying Value and Maximum Exposure (Details) - USD ($) | Sep. 30, 2023 | Dec. 31, 2022
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Accounts Notes And Loans Receivable [Line Items] |  |
Available for Sale Security and Property Loan Receivable, Maximum Exposure | $ 515,304,516 | $ 667,698,183
Mortgage Revenue Bonds [Member] |  |
Accounts Notes And Loans Receivable [Line Items] |  |
Available for Sale Security and Property Loan Receivable, Maximum Exposure | 87,872,616 | 71,629,581
Taxable Mortgage Revenue Bonds [Member] |  |
Accounts Notes And Loans Receivable [Line Items] |  |
Available for Sale Security and Property Loan Receivable, Maximum Exposure | 10,526,681 | 3,044,829
Governmental Issuer Loans [Member] |  |
Accounts Notes And Loans Receivable [Line Items] |  |
Available for Sale Security and Property Loan Receivable, Maximum Exposure | 195,547,300 | 300,230,435
Taxable Governmental Issuer Loans [Member] |  |
Accounts Notes And Loans Receivable [Line Items] |  |
Available for Sale Security and Property Loan Receivable, Maximum Exposure | 13,573,000 | 8,000,000
Property Loans [Member] |  |
Accounts Notes And Loans Receivable [Line Items] |  |
Available for Sale Security and Property Loan Receivable, Maximum Exposure | 89,260,250 | 169,002,497
Investments in Unconsolidated Entities [Member] |  |
Accounts Notes And Loans Receivable [Line Items] |  |
Available for Sale Security and Property Loan Receivable, Maximum Exposure | $ 118,524,669 | $ 115,790,841

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- Definition Available for Sale Security and Property Loan Receivable, Maximum Exposure - This represents the maximum exposure to loss related to the Available for Sale Securities and Property Loan Receivables. + References No definition available. + Details
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Namespace Prefix: | ghi_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | instant

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- Definition 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. + References No definition available. + Details
Name: | us-gaap_AccountsNotesAndLoansReceivableLineItems
Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

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- Details
Name: | us-gaap_InformationByCategoryOfDebtSecurityAxis=us-gaap_AvailableforsaleSecuritiesMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_InformationByCategoryOfDebtSecurityAxis=ghi_TaxableMortgageRevenueBondsMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_InformationByCategoryOfDebtSecurityAxis=ghi_GovernmentalIssuerLoanMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_InformationByCategoryOfDebtSecurityAxis=ghi_TaxableGovernmentalIssuerLoanMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_InformationByCategoryOfDebtSecurityAxis=ghi_PropertyLoansMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_FairValueByAssetClassAxis=us-gaap_EquityMethodInvestmentsMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |