Self-assembled materials are attractive for next-generation membranes. However, the need to align selfassembled nanostructures (e.g. cylinders, lamellae) and the narrow stability windows for ordered bicontinuous systems present serious challenges. We propose and demonstrate a novel approach that circumvents these challenges by exploiting size-selective transport in the water-continuous medium of a nanostructured polymer templated from a self-assembled lyotropic H1 mesophase. Optimization of the mesophase composition enables high-fidelity retention of the H1 structure on photoinduced cross-linking. The resulting material is a mechanically robust nanostructured polymer possessing internally and externally cross-linked nanofibrils surrounded by a continuous aqueous medium. Fabricated membranes show size selectivity at the 1- to 2-nm length scale and water permeabilities of ~10 liters m-2 hour-1 bar-1 mm. Moreover, the membranes display excellent antimicrobial properties due to the quaternary ammonium groups on the nanofibril surfaces. These results represent a breakthrough for the potential use of polymerized lyotropic mesophase membranes in practical water purification applications.