Hello XXXXXXXXXX:
In a divorce, you would normally be entitled to an equitable distribution of all assets acquired during the marriage and this would include a portion of the equity in the home that you helped to create. Equitable does not necessarily mean equal though, and your Husband may be entitled to a special equity for any monies he invested in the home prior to the marriage, since this was his pre-marital investment.
Also, I am guessing that the Deed conveys the real property from your Husband as Grantor to you and him as Grantees, in which case you legally hold a 1/2 interest in the home.
So regardless of his assertion that you are only paying rent, I believe you have a very strong claim to one half of the property, minus any special equity he has in the home, in the event of a divorce. If he were to pass away, the intestate laws of most jurisdictions provide the surviving spouse with at least a life estate interest in the home. This means you can live there for the rest of your life and upon your death the property would pass to the Remainder persons.
On last thing, if your relationship improves I would suggest that you talk to him about a mortgage insurance policy that pays the remaining mortgage balance in full in the event of his untimely death.
I hope this helps, best of luck!
MDonnelly
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Former State Prosecutor, criminal defense, family law, real estate, & civil litigation