An appliance includes a housing defining an interior cabinet, a crisper drawer disposed therein, and a circulation system. The crisper drawer includes a base, walls, and lid defining a cavity, the lid selectively closing the drawer to limit air flow to and from the cavity. One or more of the base, the walls, and the lid define an opening for a humidity membrane disposed therein, sealed in the opening. The membrane includes nanofibers dispersed in a matrix to provide pervaporation across the membrane for airflow from the cavity to the interior cabinet. The circulation system cooperates with the membrane, and includes one or more fans disposed within the drawer to selectively facilitate air flow across the membrane and mix air within the cavity to control a humidity level within the drawer.