An insulation system for an appliance includes a first vacuum insulated structure having a first set of sidewalls that define a first refrigerating compartment, a second vacuum insulated structure having a second set of sidewalls that define a second refrigerating compartment and a medial insulation structure having a rigid perimeter wall. The rigid perimeter wall includes a front portion that defines at least one hinge support adapted to support an appliance door. The rigid perimeter wall defines an insulating cavity that is filled with an insulating material. The first vacuum insulated structure engages a first edge of the perimeter wall and the second vacuum insulated structure engages a second edge of the perimeter wall.