Am I legally obligated to pay off my late brother's half of the mortgage?
A deceased's debts should be paid with the property in their estate (the property left at their death). Children/siblings don't inherit their parent's debts unless they created a co-signor/guarantor/surety/joint account relationship to the debt, so that the child's/siblings name is on the debt also, and it isn't a separate debt. Spouses will generally only be liable for a separate debt of the deceased if they live in a community property state. However, state laws vary about which marriage partner is responsible for certain debts, depending upon when the debt was incurred, the identity of the debtor, or the purpose of the debt.
Only after the debts are paid will the remaining assets be distributed among the beneficiaries of the will. Be advised that when a child inherits property that is collateral for a debt -- for example, a car that is not paid for or a house with a mortgage -- the debt comes with the property. If there is insufficient money or assets to pay all creditors, then the estate must be divided up as equally as possible, with secured creditors receiving priority. This means that if the deceased parent died with little or no money in their accounts and didn't own a home, unsecured debt, such as credit card debt will not be paid to the creditors.