An insulating structure for an appliance includes a trim breaker, a wrapper, and a liner. The wrapper and liner coupled to the trim breaker and at least partially defining a structural cabinet. A barrier is positioned between the liner and the wrapper. The barrier is also coupled to the trim breaker. An inner compressible gasket is proximate the liner, and an outer gasket is proximate the wrapper. The inner gasket and the outer compressible gasket are coupled to the barrier.