WASHINGTON—The House of Representatives unanimously passed a series of bills supporting protesters in Hong Kong who have called for democratic reforms in the city, delivering a rebuke to Beijing for what the U.S. lawmakers called a corrosion of individual freedoms in the territory.

Demonstrations in Hong Kong began this summer in response to a since-abandoned bill that would have allowed extradition into mainland China’s legal system, growing into a broader protest for democratic overhaul and a probe of police conduct. Most...