I listen to Dave Ramsey everyday so I will try to explain how it works. I am sorry you are facing this difficult situation.
The debt is not forgiven or written off except for student loans. Spouses or other relatives are not responsible for the decedent's debt automatically but the estate distributes the assets of your spouse. But before the assets can be distributed to anyone, all debts must be paid by the executors.
After the debts are paid from with the remaining assets such as a house or car, the remaining assets will go to any beneficiaries.
Now if there are no assets Chase can not collect the debt from other family members or children. In some states the creditor can not collect from the spouse either. But in a community property state it gets more complex. In a community state, the spouse is responsible. I would suggest you consult a attorney before you go ahead so you will have all your ducks in a row since estate law is very detailed, complex and laws can change.
I found a few articles that make help explain it more.
What Happens to Debt After Death? - Estate Planning - Law and Daily Life
What Happens to Credit Card Debt After Death?
What to Do After My Spouse Died & Left Me Credit Card Bills I Didn't Know About | eHow.com