It could be owned jointly by you and him, but don't let him be the sole owner. This is just in case something happens later that would leave you without anything. It's not that you don't trust him but just a sensible way to arrange things now to avoid trouble later. And remember that he is married to another woman and as she grows older she might need help, and he will feel obliged. She will forever be a part of your extended family.
Life is never simple.
Take your happiness where you find it but know that it's not always a bowl of cherries.