Microphase separation in a binary blend of oppositely charged polymers can in principle be stabilized electrostatically without the need for connected block polymer architectures. This provides a route to control microstructure via parameters such as polymer charge density, salt concentration, and dielectric constant. Here, we use an equilibrium self-consistent field theory to study the phase behavior of such a binary blend, with or without counterions and added salt, and show that it exhibits the canonical ordered phases of a diblock copolymer melt. We demonstrate how differences in the charge density and the dielectric constant of the two polymers affect phase behavior in this system. In particular, we find that the phase windows for sphere phases are dramatically affected and that the Frank-Kasper phases sigma and A15 can be stabilized when the minority component has a higher dielectric constant than the surrounding matrix. Since the domain length scale in this system is determined electrostatically and is not subject to chain-stretching limitations imposed by block architectures, our results suggest a possible route to large-unit-cell complex-sphere phases. These predictions will be most easily tested in oppositely charged polymeric ionic liquids, where the bulky and de-localized charges should aid equilibration in a solvent-free environment.