Affordable Housing Opportunities Made Equitable Act or the Affordable HOME Act This bill addresses the availability and affordability of housing. Among other provisions for low-income and homeless individuals, the bill requires the Department of Housing and Urban Development (HUD) to construct and preserve multifamily rental housing projects in rural areas, specifies the number of low-income housing choice vouchers HUD must provide in FY2022-2031, and provides FY2022-2031 appropriations for HUD to assist permanent supportive housing. The bill also repeals the limitation on construction of new public housing units, commonly known as the Faircloth limit or the Faircloth amendment; prohibits discrimination in housing based on source of income; and provides additional FY2021 appropriations for the Housing Trust Fund, which provides assistance to states to produce and preserve affordable housing. For individuals experiencing unemployment or income shortfalls during periods of increased state unemployment or during certain disasters, the bill establishes an emergency assistance fund to provide housing assistance. For qualifying homeowners, the bill requires HUD to provide grants for down payment assistance and establishes a 15% annual mortgage interest tax credit. Among other provisions for residential renters, the bill requires notice and specific cause for eviction, provides funding to state and local governments that have established a right to counsel in certain housing cases, and requires certain landlords to provide renters an opportunity to purchase before selling or transferring the rental property. The bill also provides grants for acquisition and preservation of manufactured home communities.