Military Construction, Veterans Affairs, and Related Agencies Appropriations Act, 2020 This bill provides FY2020 appropriations for military construction, the Department of Veterans Affairs (VA), and related agencies. The bill provides appropriations to the Department of Defense (DOD) for military construction for the Army; the Navy and Marine Corps; the Air Force; Defense-wide agencies and activities; the Army and Air National Guard; and the Army, Navy, and Air Force Reserves. The bill also provides appropriations to DOD for the North Atlantic Treaty Organization (NATO) Security Investment Program; the Base Closure Account; Construction and Operation and Maintenance of Family Housing for the Army, the Navy and Marine Corps, the Air Force, and Defense-wide agencies and activities; the Family Housing Improvement Fund; and the Military Unaccompanied Housing Improvement Fund. The bill provides appropriations to the VA for the Veterans Benefits Administration, the Veterans Health Administration, the National Cemetery Administration, and Departmental Administration. The bill provides appropriations for related agencies and programs, including the American Battle Monuments Commission, the U.S. Court of Appeals for Veterans Claims, Cemeterial Expenses of the Army, and the Armed Forces Retirement Home. The bill provides appropriations to specified DOD military construction accounts for (1) Overseas Contingency Operations, and (2) Natural Disaster Relief. The bill also sets forth requirements and restrictions for using funds provided by this and other appropriations Acts.