Keep the girlfriend out! Man I can see this getting ugly.
All the houses should be under his name. They don't live together and won't for a while, being co-owners fucks shit up.
She'll let him do this because if she truly trusts him, it's not an issue.
"The most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents... some day the piecing together of dissociated knowledge will open up such terrifying vistas of reality, and of our frightful position therein, that we shall either go mad from the revelation or flee from the light into the peace and safety of a new Dark Age."
-H.P. Lovecraft