I am sorry for your loss. Unpaid medical bills along with other debts of a decedent are generally paid from the person's estate. All the individual's assets pass to the estate upon death and debts are settled using assets in the estate.
If you are named executor or personal representative of the estate, you are not personally liable for debts of the estate. They are settled using estate assets. If there are insufficient assets in the estate to settle all the debts, the debts remain unpaid and the creditor would generally have to write them off.
An exception is if you signed an agreement to guarantee payment of the medical bills or to be jointly responsible for them.
I agree with my colleague. Under Maine law, you are not responsible for your husband's debts unless it is a joint debt or you guaranteed the debt, in this case medical bills. I am sorry for your loss but I hope these answers remove some worry from your mind.