Grammar: use of "mine" or "my" in the following sentence: "My/mine and Harriet's house"?

Niether ""My and Harriet's house" nor "Mine and Harriet's house" is correct English. Grammatically, it would have to be "Harriet's and my house", but all three of these sentences sound very awkward and clumsy, and would best be expressed be rephrasing: "The house belonging/which belongs to Harriet and me" or "The house where Harriet and I live", or something along those lines would be better.