Front-of-house is the part of a theatre or hotel that the public walks through and uses: the foyer, the ticket desk, the bar, the lobby, the seats — not backstage, not the kitchens, not the staff-only corridors. In a theatre, front of house is everything on the audience’s side of the curtain; back of house is where the show is built. Hotels use it the same way: guests at the front, staff work at the back. Though actually, restaurants stole the phrase too: waiters work front of house and cooks work back of house. That use is about jobs, not rooms — a neighbouring use, not a different spelling. The sense here is the public areas themselves. It is workplace English. It is not something you say about a family home.