Mental Health for Heroes' Families Act of 2008 - Removes the requirement that, in order for family members of a veteran being treated in a Department of Veterans Affairs (VA) hospital for a non-service-connected disability to be eligible for counseling, training, and mental health services in connection with the veteran's treatment: (1) such services must have been initiated during the veteran's hospitalization; and (2) the continued provision of such services on an outpatient basis is essential to permit the veteran's discharge from the hospital.