Nonionic diblock copolymers, with a highly asymmetric relative composition (f), microphase segregate into structures in which the minority component always forms cylindrical or spherical domains that are embedded in the majority component continuous matrix phase. Recently, a hybrid liquid state theory (called the DHEMSA approximation) and self-consistent field approach for ionic diblock copolymers have demonstrated the possible existence of "inverted" phases in which the minority ionic component forms the continuous matrix phase and the majority nonionic component forms cylindrical domains. We find that such anomalous behavior is closely related to the thermodynamics of phase segregation found in a blend of an ionic polymer and a nonionic polymer at the electrostatic coupling values typical of polymers in the molten state, at which nonionic and ionic polymers segregate into two partially miscible phases. This partial miscibility holds even across infinite molecular weights of the polymers. Such partial miscibility causes swelling of the minority component and a "switch" between minority and majority phases in ionic block copolymer melts. By combining the DHEMSA approximation with the Helfand-Tagami theory, we calculate the interfacial tension gamma between coexisting phases of ionomers. The full phase diagram for ionomer blends and gamma allows us to construct the phase diagram of block copolymers. In addition to the conventional microphases found in nonionic diblock copolymers, we find microphases with "inverted" cylindrical and spherical domains. We also predict an "inverted" phase at high values off where the nonionic minority component becomes swollen by the ionic component and forms the matrix phase. Three-dimensional self-consistent field theory modeling confirms the existence of the "inverted" bicontinuous phases between the lamella and the inverted cylinder microphase regions of the phase diagram.