Responsibility for my deceased spouse's debts

I am not admitted in Georgia.  I am sorry for your loss.

Generally, the estate of the decedent is responsible for the his or her debt, not family members.  A line of credit can differ from a credit card.  It is can be secured debt - like against the house - but can also be unsecured in some circumstances where checks are written against a cash amount. 

Did your husband use the house to secure the line of credit?  I am assuming that it is in both your names.  You should seek legal help in your area and have all the information necessary for the attorney to look at and determine.  Good luck.