A dishwasher includes a tub having a bottom wall and a plurality of side walls that collectively define a first washing chamber. The tub is supported in an outer, modular support body having first and second opposing side walls joined by a bottom wall, as well as a pair of upper frame members. In one embodiment of the invention, first and second support bodies are mounted one atop another to establish a dual drawer-type dishwasher, with the first and second support bodies being joined, preferably at a stepped interface region, by a plurality of brackets. The first and second support bodies are preferably aligned by arranging lugs formed on upper in-turned flanges on a lower support body within recesses formed in the bottom wall of the upper support body.