In unusual bipartisan fashion, the House on Wednesday approved a three-year $58-billion compromise bill intended to revive NASA's manned-exploration programs while funding plans for pioneering private rockets able to blast astronauts into orbit.

Capping nearly a year of intense industry turmoil, agency uncertainty and congressional debate, the vote reflected last-minute decisions by House leaders from both parties to embrace a previously-passed Senate blueprint for NASA, though it doesn't completely satisfy any of the rival...