Abstract: A soft-sided container assembly is provided that includes a beverage container liner and an insulating cover for generally maintaining the temperature of the container contents during transport and/or short term storage. The container assembly is adapted to facilitate access to and/or removal of the container liner from the insulating cover. Thus, the top panel of the insulating cover is provided as a cover flap structure having a container overlying portion and a flap attachment portion that is detachably secured may be attached to the side wall. Because the top panel overlies substantially the entire exposed top wall of the container liner, detaching the top panel substantially fully opens the cover for removal of liner. In addition or in the alternative, one or more grip structures are provided adjacent the bottom of the insulating cover, for being manually grasped, to provide suitable resistance whereby the liner can be removed from the cover.