The present invention provides for an improved trim part with a multi-feel cover for use in a trim assembly, e.g. a door panel, and to a continuous two-shot molding operation that may be performed utilizing a single mold assembly. In an exemplary embodiment, a trim assembly includes a substrate having an integrated armrest and/or integrated bolster formed by injecting a first material into a first shot mold cavity in a first shot of a molding operation. A cover then is molded to at least a portion of the integrated trim part by injecting into a mold chamber a second foamed material in a second shot of the molding operation. The molded cover defines a first and second thickness with the second thickness being greater than the first thickness to provide a softer feel. The second foamed material produces an outer skin and a light, cellular inner core, within at least the second thickness of the cover, such that the skin deforms and compresses the inner core when a force is applied thereby providing a softer feel.