No matter where the money is from, if you take money and place it in real estate, like your house, and it is jointly titled, the court will “presume” that you “gifted” the funds to the marriage by putting them in a house that is jointly titled. This is a hard presumption to overcome.
Therefore, if you jointly title the house it is considered a gift to the marriage. However, the fact that you purchased it with your separate property may be a justification for an unequal distribution. However, if he has reduced the principal on the mortgage during the marriage, then the reduction in the principal on the mortgage would be marital property. He would also be entitled to any increase in value that was caused because of his active efforts, such as installing new floors, upgrades etc. Although, it doesn’t sound like he contributed anything financially or through sweat equity, so you would likely have a good claim for unequal distribution. Increases in value that occur simply because of market forces are not marital property.
Since his name is not on the mortgage you will not have to refinance the loan, he will simply need to sign a new deed which transfers his ownership interest to you. He may demand some of your equity though (if you have any) in exchange.
I would recommend you schedule at least a consultation with an attorney to give you a plan of action moving forward. Good luck.