@Barry *****
A house on land, not a condo, can not be completely on the name of a non Thai.
Theoretically as a foreigner you can own the house, but not the land, making it a bit complicated with an existing house.
When the Thai wife buys land, and give usufruct to the non Thai husband for 30 years, he can build a house on it on his name.
The usufruct is also in other cases the best way to give some certainty to the non Thai partner.