This question is determined by state law so you have to look at the property law of your particular state. It may be that the signature of the non-owner spouse is invalid, but I'm not sure that would invalidate the mortgage unless there is a quirk in state law that says the mortgage is only valid if signed only by the property owners.
There is another aspect of marital property interests: inchoate property interests. This is based on the presumption that the spouse is the primary heir and therefore has an inchoate (unformed) interest in property owned solely by the spouse. States differ on this, particularly in whether it applies to real and personal property differently.
So, the best thing you can do is get an attorney's opinion.