A possibility of microphase separation in a blend of oppositely charged polyelectrolytes, being immiscible when uncharged, is studied theoretically and by means of dissipative particle dynamics (DPD) simulations. Emerging microstructures are stabilized by an excess Coulomb energy preventing an unlimited growth of oppositely charged domains. Strong segregation theory of microphase separation is developed, and the predicted dependence of the microstructure period on the Flory-Huggins incompatibility parameter, D similar to chi(1/6), is confirmed in the DPD simulations. The effect of the blend composition on the morphology of the segregated structures is found to be similar to the one observed in nonionic diblock copolymers. Namely, a symmetric blend with equal volume fractions of the components is lamellar; an increasing asymmetry of the components results in lamellae -> perforated lamellae -> bicontinuous structures -> hexagonally packed cylinders -> bcc structure transitions. Similarities and distinctions between this type of microphase separation and that in block copolymers are discussed.