If your husband died, his half of the property would go to his heirs….probably and most likely his children; unless he leaves his half to a specified person in his last will and testament. No, you will not automatically get his half….one-half (50%-community property laws) is yours. You would have to purchase his one-half from his heirs or sell your one-half to them. Or you and his heirs may be mutually willing to sell the property and split the money. So the best way to ensure that you keep the house is to get last will and testaments for both of you as everything you own together is only 50% yours and his.
This is Texas law. I am not sure if other states would have different laws or not.
You should consult an attorney in your state.