The property is owned by the two of you. You need to look at the deed that came out of the probate. It most likely just has your two names on it, which is tenancy in common. When one of you dies, the other keeps his half and any will or rules of intestate succession determines how the other half passes. The two of you could deed it to yourselves as joint tenants which means that the other one would receive entire ownership at the death of the others.
If he dies before you, then when his estate is probated it most likely will be split between the spouse (if any) and the children if there is no will to the contrary. Your "upkeep" won't much enter into it.

