Military Housing Affordability Act of 2022 This bill extends certain authorities of the Department of Defense (DOD) to adjust basic housing allowances for military housing in certain areas. Specifically, the bill extends to December 31, 2024, DOD's authority to increase the rates of basic housing allowance in areas of a declared major disaster or areas containing one or more military installations that are experiencing a sudden increase in the number of members assigned to the installation. The bill also extends to September 30, 2024, DOD's authority to prescribe a temporary adjustment to basic housing allowance rates if DOD determines the costs of adequate housing for civilians in that military housing area differs from the current allowance rates by more than 20%.