My husband died without a will, and I transfered the mortgage to my name, am I responsible for his and his only credit debt?

The house should have been probated, and the debt would have been resolved at that time. By just putting the mortgage in your name, (which is odd -- usually the mortgage holder would have also required the home be in your name for you to assume the debt ....) you have only done half the process.

YOU personally would not be liable for his sole debt assuming you did not use the credit cards, but the HOUSE may be attachable by his creditors if it is still in his name, and they may open Probate as a creditor to try to do just that. In other words, they may not be able to collect from you, however they can force the sale of the house and you could lose your place to live (and the Mortgage Company can still come after you if the house is not sold for the full debt amount.)

You need to contact a local attorney familiar with the Probate process to guide you through the process ASAP, and see if there might be other ways to protect yourself at this point.