A soft-sided insulated container assembly has a first insulated portion and a second insulated portion. The first and second insulated portions are generally box-shaped and are mounted in a back-to-back arrangement, such that they share a common wall. One of the portions has a receptacle in the nature of a removable, non-collapsible molded plastic tub, or bucket, that also has a mating, removable, multi-positional divider mounted therein. The molded plastic receptacle is substantially rigid and functions to provide a stiff internal structure within the surrounding soft-sided wall structure. The other portion is foldable, and can be moved between a collapsed, out of use position, to an expanded position for use when the main receptacle is not sufficiently capacious for all objects, or when different objects are better kept at different environmental conditions. The foldable portion is provided with securing straps to keep it neatly in the folded position when not in use.