"Rumah saya adalah rumahmu."
Terjemahan:My house is your house.
House kata benda, jadi ada bentuk fisiknya, contohnya Bias house. Berbeda dengan home, home lebih ke "feeling/koneksi", contoh: Bandung is my home.
I don't think there's a difference in the context of this sentence, so if you wrote "My home is your home," it should be accepted.
But generally, "home" is the place where you live (where you feel "at home") whereas "house" means only the building or structure.