We report a simple photo-cross-linking process to chemically arrest the different liquid-crystalline structures formed by self-assembly of wedge-shaped amphiphilic mesogens. Using this route, we obtained free-standing polymer membranes with columnar or bicontinuous cubic structures, depending primarily on the relative humidity conditions during UV-induced cross-linking. These cross-linked mesostructures show much higher thermal stability in comparison with that of the liquid-crystalline structures of the initial monomers. The ionic conductivity of the membranes strongly depends on the water uptake preceding the polymerization reaction. According to NMR diffusometry, which can quantify water transport in one or two environments in these materials, the water diffusion rate in the membrane with bicontinuous cubic structures can approach values of commercial ion conducting membranes. These studies show promise for use of this fabrication route in practical applications for selective ion and water transport.