The morphology and conductivity of poly(styrenephosphonate-b-methylbutylene) block copolymers containing ionic liquids are investigated. The block copolymers display a series of well-defined self-assembled morphologies, i.e., lamellae, gyroid, hexagonal cylinder (HEX), body-centered cubic, and A15 lattice, in the absence and presence of ionic liquids. The observation of an equilibrium A15 lattice for linear diblock copolymers, in contrast to a number of theoretical studies, is ascribed to the packing frustration accompanied by prevailing electrostatic interactions. The samples having the A15 lattice show a substantially higher morphology factors (0.83-0.96) than those with the HEX phases (0.42-0.69). This indicates the structural advantage of the A15 lattice with a well-defined 3D symmetry over the 2D HEX structure for constructing less tortuous ion-conduction pathways. This unprecedented study portends the rational design of nanostructured phosphonated polymer membranes with improved conductivity.