After my husband passes away, will I be liable for debt in his name only?

First of all, I'm sorry to hear of your situation.

Generally, one spouse is not obligated to pay the debts of the other spouse.  However, there are several exceptions to this rule.  The first exception as to do with just where you live.  If you live in a community property state, you would typically bear responsibility for such a debt.  However, IL is not such a state.  The second exception would be if you signed (or in some other way) agreed to be legally bound for re-payments on the debt.  For example, if upon your spouse’s admission to the hospital, you signed (or co-signed) any papers that would obligate you for payment of any bills incurred during your spouse’s hospital stay. This is true no matter what state that you live in. The last exception falls under something called the "doctrine of necessaries" which was established at common law.  While many states no longer follow it, some states do. Under this doctrine, one spouse is liable for the "necessary" expenses incurred by the other spouse during marriage.  This holds true for any debt but particularly for medical bills which are deemed to almost always be “necessary”.  My understanding is that IL has such a law.

Also, in the case of a deceased spouse, even in a situation that did not fall into one of the above exceptions, the deceased’s estate would still be liable for repayment; therefore indirectly a surviving spouse could be affected financially.  At this point, you may want to consult directly with an attorney in your area.  They can best advise you of all or rights as they exist under state law and has they may be affected by other factors.