Families may be eligible to receive support pursuant to sections 68-1501 to 68-1519 if the family (1) resides in the State of Nebraska, (2) has a family member who is disabled and is (a) living at home or (b) residing in a state or private institutional or residential facility but could return home under sections 68-1501 to 68-1519, and (3) has insufficient income to provide for the total cost of care for the disabled family member.