Substance Use Disorder and Family Engagement in Recovery Act or the SAFE in Recovery Act This bill expands services available to families affected by substance use disorders (SUD) and implements protections for parents seeking SUD treatment. Specifically, the bill requires health centers funded through the Community Health Center Fund (CHC Fund) to provide mental health and SUD treatment services, and provides funds to the Department of Health and Human Services (HHS) to implement this change in FY2025. The bill also reauthorizes the CHC Fund through FY2028. Moreover, under the Opioid Use Disorder Treatment Demonstration Program, the bill permits HHS to provide increased per-beneficiary payments for beneficiaries receiving pregnancy or postpartum services. As a condition of Maternal and Child Health Services Block Grant funding, the bill restricts states from investigating and reporting pregnant and postpartum patients affected by SUD in specified instances. For example, the results of toxicology testing on patients taking prescription drugs (including drugs that treat SUD) in accordance with the recommendations of the prescribing doctor may not be the sole factor in a family separation determination. Further, states may not investigate a patient for child neglect or abuse, nor report them to a child protective services system, solely on account of their use of a prescription drug. Finally, the bill establishes new federal efforts to study and fund care for families affected by SUD, including a consortium led by the National Institutes of Health to set research priorities related to SUD.