Housing is Infrastructure Act of 2021 This bill generally addresses housing affordability and infrastructure. The bill authorizes the Department of Housing and Urban Development (HUD) to provide grants, programs, and other support related to public housing, affordable housing preservation and construction, and mortgage access. The bill also establishes and funds the National Investment Authority (NIA) which must design, finance, and implement a strategy of long-term national economic growth and development. The NIA must select projects that coordinate investment of public and private capital in equitable, inclusive, and sustainable growth of the economy. Furthermore, the bill establishes the National Infrastructure Bank (NIB) to implement the strategy by engaging in credit market activities that support public and private investment in critical public infrastructure projects. The bill gives the NIA bond issuing authority and authorizes the Board of Governors of the Federal Reserve System to purchase these bonds. The Federal Reserve must lend funds on a short-term basis upon the request of the NIB and other subsidiaries. Additionally, the Department of the Treasury must provide for a line of credit not to exceed 100% of the NIA's total assets. Finally, the bill (1) authorizes HUD to provide support for fair housing organizations, and (2) requires consultation with a fair housing enforcement organization as part of an application for certain housing grants or funds.