The phase behavior and microstructure of copper(II) bis(2-ethylhexyl) sulfosuccinate, Cu(AOT)(2)-isooctane-water, is determined over a wider domain than previously used. It is characterized by a rich variety of phases and microstructures. Equilibrium phases consisting of spontaneous thermodynamically stable emulsions in equilibrium with other microstructure phases are observed. These spontaneous emulsions are composed of supra-aggregates, lamellar spherulites in which the interior and exterior are phases of interconnected cylindrical nanostructures. In another part of the phase diagram, clumps of interdigitated micelles are surrounded by an interconnected cylinder phase. The phase boundaries emerge qualitatively from elementary considerations that require only notions of local and global packing constraints.