The action was largely symbolic since the president would be all but certain to veto the bill, but the bipartisan vote reflected resistance within his own ranks on his signature issue.
The Commission of Fine Arts, a Trump-aligned advisory body, granted preliminary approval. But its vice chairman suggested losing statues atop the structure and other revisions before a final vote.
Thursday's vote marked the fourth time this Congress that a handful of Republicans teamed up with Democrats to force a House vote on legislation opposed by GOP leadership.
A federal judge wrote that an exception he made for work on security features did not cover most of the construction on the larger ballroom project Trump has proposed.