Reuniting Families Act This bill amends the Immigration and Nationality Act (INA) to recapture unused employment-based and family-sponsored visas from FY1992-FY2016; reclassify spouses, permanent partners, minor children, and stepchildren of permanent residents as immediate relatives; repeal the per-country immigration limits; repeal specified bars to reentry and allow waivers of inadmissibility to promote family unity; exempt children of naturalized Filipino veterans from immigration limitations; and allow relatives of a deceased alien to maintain visa eligibility. The bill defines "permanent partner" to purposes of applying the INA to LGBT families and individuals.