Backlog Elimination, Legal Immigration, and Employment Visa Enhancement Act or the BELIEVE Act This bill increases maximum limits on employment-based visas and makes other related changes. The bill increases the worldwide cap on employment-based immigrants admitted each fiscal year, from 140,000 plus certain additions to 270,000 plus the same additions. The bill (1) eliminates existing per-country caps on employment-based immigrants, (2) allows certain employment-based immigrants to comprise a higher percentage of the worldwide level of immigration in a fiscal year than under current law, (3) exempts from numerical caps immigrants coming to work in the United States as physical therapists or professional nurses, and (4) exempts from numerical caps a qualifying alien who graduated from a U.S. institution of higher education and who was admitted into the United States as a dependent of a nonimmigrant. The bill provides various immigration-related benefits, such as work authorization and exemption from certain numerical limits, to qualifying spouses and children of employment-based immigrants. An alien who has properly filed for permanent legal resident status and is awaiting a visa number becoming available shall have lawful status and employment authorization while the application is pending, subject to requirements such as a background check.