My mother passed away last month with a mortgaged house, how can my brother and I assume the mortgage?

Typcially, when a mortgaged property changes ownership, the mortgage lender has the right to demand full payment of the mortgage balance. This is due to something known as a "due on sale" clause. This clause allows a lender to call the mortgage due if a house becomes titled in another person's name. However, when a mortgaged home is inherited, the person who inherits gets it automatically takes over the loan; there is no need for a credit check or employment verification. Legally, in this scenario, a lender can't call the mortgage due as long the monthly payments are made on time.

You most likely cannot assume the mortgage: most mortgages have provisions which do not allow assumption. In theory, the lender could agree to allow you to assume it, since the parties to a contract (and that's what a mortgage is: a contract) can modify it by mutual consent. In practice, that will most likely not happen, especially if your credit is just "fair": lenders want the fees from refinancing and/or new mortgages, and also will not let someone with only fair credit take over an existing mortgage. You can ask, but the lender doesn't need to let you assume the mortgage, and if they don't and the mortgage has some no assumption clause or provision, there is nothing you can do about it--those clauses are completely legal and enforceable.