There is much implied in your message regarding the house. My observation will assume that the present market value of your husband's property is at or less than the balance of the mortgage(s). I will also assume the title of the house has no future interest (i.e., is not tied-up in a life estate, etc.) You do not mention life insurance your spouse may have, which if you are the beneficiary could use to bring the mortgage current.
Assuming the above, and assuming your spouse's prognosis is dire, neither you nor your spouse have an incentive to change the status quo regarding the property. Here is why:
Deceased Spouse's Debt
Some people assume a decedent's debt is forgiven or possibly written off by creditors. The law does not work that way, with the exception of federal student loans. However, spouses or other relatives are not responsible for the decedent's debt automatically, either. Many collection agents take advantage of a debtor's grief and ignorance of the law to imply the family must pay the decedent's debt, but that may not be the case.
When a person dies with a will, the will controls the financial affairs of the decedent's assets, which is called the "estate." A will distributes assets, not debts. However, before any assets can be distributed to the heirs, all known debts must be paid by the executor. Therefore, the executor will sell assets in the estate to pay for any debts that remain. Only after the debts are paid will the remaining assets be distributed among the beneficiaries of the will.
If a person dies without a will, this is known as "dying intestate" in lawyer-speak. In this situation, the court appoints an administrator to handle the distribution of the decedent's assets according to the laws of the state. As with dying with a will, assets are distributed after debts are paid.
Here is a key point: If the estate is insolvent the creditor has no legal right to collect the debt from family members, children, or friends. There is no feudal debt bondage that ensnares an entire family, at least not in the US. In most states, the creditor cannot collect from the spouse either. However, in community property states, the question becomes more complicated.
Deceased Spouse's Debt in Community Property States
Community property states include Alaska, Arizona, California, Idaho, Louisiana, Nevada, New Mexico, Texas, Washington, and Wisconsin. Generally speaking, in community property states, debt incurred by a spouse for the benefit of the family is considered a "community" debt, and therefore the spouse is responsible for repaying that debt.
Alas, no two community property states use exactly the same laws.
The interesting issue in this case is the house was purchased before the marriage. It is likely community income was used to pay the mortgage during the course of the marriage. Were this a divorce, you and your spouse would be dividing the ownership of the house according to the amount that the community had contributed to the mortgage. However, where the question is of a term I will call "community liability" for an expected deficiency balance, I am uncertain if Washington recognizes that theory.
If under Washington law the community has no liability for a deceased spouse's mortgage, and the liability is upon the decedent's estate alone, then as I mentioned earlier you should leave the house titled in your spouse's name and not try to refinance. That is, of course, if you want to free yourself of the liability of the mortgage.
It is imperative that you consult with an attorney in Washington state so that you understand your rights and liabilities in your particular circumstances. In particular, bring the title of the house to the attorney so that he or she can see if it is in your husband's name only, or if you are named in a future interest. If you are named in a future interest, then the property may pass to you as a matter of law are outside of the probate process, and are not part of the deceased estate. Whether this brings a liability for you regarding the mortgage is unclear to me. Again, this is a question for a Washington attorney to answer.
For additional general information, see the Federal Trade Commission documents Paying the Debts of a Deceased Relative: Who Is Responsible? and FTC Issues Final Policy Statement on Collecting Debts of the Deceased.
I hope this information helps you Find. Learn & Save.