Gemini-type amphiphiles with benzylimidazolium-based zwitterionic head-groups have been newly designed and synthesized. They co-organize into liquid-crystalline ordered states with various acids owing to the nature of the zwitterionic parts to cause ion exchanges with these acids. Their co-organization behaviors can be tuned by various factors including the linker selection between the head-groups, the length of the long alkyl chains, the acid species, and the molar ratio between the zwitterions and acids. By tuning these factors, we have succeeded in preparing amphiphilic zwitterion/acid mixtures that form bicontinuous cubic liquid-crystalline assemblies with a 3D continuous hydrophilic surface. These cubic liquid crystals function as ion transporting matrices whose ionic conductivities are enhanced owing to the presence of a 3D continuous proton conduction pathway along the hydrophilic surface. The present material design would possess a great potential to bring an innovation to the design of proton conductive polymer electrolytes.