Will I get to keep our house if my husband dies?

My husband and I married about 5 years ago. He is the custodial parent of his two young sons. In his divorce he was awarded the family home and they signed a quitclaim deed to have her removed and he refinanced in his name only. I moved into their home when we married and we are somewhat concerned as to what will happen to "our" home if he were to die unexpectedly while the boys are young. We basically understand that the boys will go to their mother and that I as a stepparent is considered a legal stranger to them but since I am not (as of right now) listed on the mortgage or deed to the home - do I have any legal basis for staying there? Should we get my name on the deed, refi (least desirable option right now) or can he simply will it to me? Thx - Is this your question? Add additional information