Electrochemical polymer synthesis usually forms dense films bound to the electrode. We report a single-step synthesis of large-area, ultrathin (~70-nanometer) polymeric membranes with a luffa-like, reticular cross-linked network with low density (0.5 grams per cubic centimeter). This particular membrane forms within an electric double layer in water constructed by voltage application without supporting electrolytes-in which deprotonated resorcinol and an aldehyde react three-dimensionally with a self-termination mechanism-and is spontaneously released when the voltage bias is removed. Initially rigid with a Young's modulus of 8.9 gigapascals, this membrane reversibly regains flexibility (0.5 gigapascals) upon wetting and can be used as a large-area membrane for separations. Its shape-persistent carbonization made it possible to yield ultrathin (~22-nanometer) nanoporous carbon membranes.