Legal Question in Real Estate Law in California

If he has no children, either with you or before your marriage, he is correct. If he has any children, they would get a share of ownership. Either way you unfortunately would have to go through probate court to get the house put in your name.

I don't know how good your marriage is, but the bigger red flag is what would happen in the event of divorce. At best you would have a major issue for litigation over whether you are entitled to any share in the house. Worst case it all goes to him.

Bottom line is that it is a bad idea on many levels to have the family home held in one spouse's name as sole and separate property, unless it really is entirely theirs, such as if they inherited it. If there are legitimate reasons for it to be owned only in his name, it should be put in a trust at least, so it can pass to you without the expense and hassle of probate.