Family Unity Rights and Protection Act This bill requires the Departments of Health and Human Services, Homeland Security, State, and Defense to ensure that alien children (i.e., children under the age of 18 removed from their parents or legal guardians at or near a port of entry or within 100 miles of the U.S. border pursuant to a zero tolerance policy for criminal illegal reentry) are reunited at the earliest possible date with their parents and guardians from whom they were separated. It also requires notification of parents and guardians of procedures for reuniting with such children and for the location of such children. The bill requires the creation of an electronic registry for information used to locate such alien children and their parents and guardians. The information in such registry may only be used for locating such children and may not be used in any criminal prosecution or other immigration proceeding. The bill also sets forth conditions on the termination of parental rights in immigration proceedings and requires the consolidation of asylum and immigration proceedings involving alien children.