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Variable Interest Entities - Variable Interest Entities Property Asset Carrying Value and Maximum Exposure (Details) - USD ($) | Mar. 31, 2024 | Dec. 31, 2023
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Accounts Notes And Loans Receivable [Line Items] |  |
Available for Sale Security and Property Loan Receivable, Maximum Exposure | $ 495,018,507 | $ 572,142,140
Mortgage Revenue Bonds [Member] |  |
Accounts Notes And Loans Receivable [Line Items] |  |
Available for Sale Security and Property Loan Receivable, Maximum Exposure | 120,453,758 | 98,336,213
Taxable Mortgage Revenue Bonds [Member] |  |
Accounts Notes And Loans Receivable [Line Items] |  |
Available for Sale Security and Property Loan Receivable, Maximum Exposure | 3,014,582 | 13,520,631
Governmental Issuer Loans [Member] |  |
Accounts Notes And Loans Receivable [Line Items] |  |
Available for Sale Security and Property Loan Receivable, Maximum Exposure | 185,157,300 | 202,547,300
Taxable Governmental Issuer Loans [Member] |  |
Accounts Notes And Loans Receivable [Line Items] |  |
Available for Sale Security and Property Loan Receivable, Maximum Exposure | 3,000,000 | 13,573,000
Property Loans [Member] |  |
Accounts Notes And Loans Receivable [Line Items] |  |
Available for Sale Security and Property Loan Receivable, Maximum Exposure | 38,261,960 | 107,511,750
Investments in Unconsolidated Entities [Member] |  |
Accounts Notes And Loans Receivable [Line Items] |  |
Available for Sale Security and Property Loan Receivable, Maximum Exposure | $ 145,130,907 | $ 136,653,246

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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
Name: | ghi_AvailableForSaleSecurityAndPropertyLoanReceivableMaximumExposure
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: |