Family Assistance and Child Support Enforcement Administrative Improvements Act - Title I: Aid to Families with Dependent Children - Amends part A (Aid to Families with Dependent Children) of title IV of the Social Security Act to reduce the Federal matching rate for statewide development of mechanized claims processing and information retrieval systems from 90 to 75 percent for FY 1987 through 1989 and to 50 percent of the administrative costs of such systems in subsequent years. Reduces from 50 to 25 percent the matching rate for those State per recipient administrative costs which exceed 175 percent of the national median for such costs. Title II: Child Support Enforcement - Amends part D (Child Support) of title IV of the Act to gradually reduce the Federal matching rate for the State automated child support information retrieval system from the current rate of 90 percent to 66 percent in FY 1990 and beyond. Accelerates the reduction in the matching rate for the administrative costs of child support enforcement programs to achieve a four percent reduction (to 66 percent) in FY 1987 rather than in FY 1990.