A soft sided insulated container assembly includes a first portion having an insulated, soft sided external wall structure, and an internal, substantially rigid molded plastic receptacle mounted therein. It has a cover structure that includes a reinforcement member for engaging a land region of the molded receptacle, thereby tending to yield an interface tending to have a sealing relationship. The container may also include a thermal storage element, and the container may have an accommodation for receiving the thermal storage element.