High-skilled Immigration Reform for Employment Act This bill increases the annual cap on H-1B visas (nonimmigrant visas for workers in specialty occupations) and authorizes grants for education. Specifically, the bill (1) increases the cap on such visas for each fiscal year from 65,000 to 130,000; and (2) exempts from this cap all visas for individuals with a postgraduate degree from a U.S. institution of higher education (currently, only up to 20,000 such visas are exempted each fiscal year). The bill also modifies the criteria for determining whether an employer is an H-1B-dependent employer. (Such employers are subject to additional requirements.) The Department of Education may make grants to states to support science, technology, engineering, and mathematics (commonly referred to as STEM) education.