Drug Free Mothers and Babies Act of 1988 - Directs the Secretary of Health and Human Services to: (1) carry out a program to research drug and alcohol abuse among pregnant women and its effects on their infants; and (2) establish demonstration projects for prevention, education, and treatment regarding drug and alcohol abuse relating to pregnant and postpartum women and their infants.

Authorizes the Secretary, through the Directors of the National Institute on Drug Abuse and the National Institute on Alcohol Abuse and Alcoholism, to make grants to health research facilities for such research, giving priority to projects researching widely available drugs about which exist insufficient information, including cocaine and crack.

Authorizes the Secretary, through the Director of the Office of Substance Abuse Prevention, to make grants to medical facilities for such demonstration projects, giving priority to projects for low-income women and their infants and projects designed to develop innovative approaches. Requires grants to be distributed among projects that provide inpatient, outpatient, and residential treatment.

Sets forth reporting requirements. Authorizes appropriations for FY 1989 through 1991.