The development of new membranes with high H2 separation performance under industrially relevant conditions (high temperatures and pressures) is of primary importance. For instance, these membranes may facilitate the implementation of energy-efficient precombustion CO2 capture or reduce energy intensity in other industrial processes such as ammonia synthesis. We report a facile synthetic protocol based on interfacial polymerization for the fabrication of supported benzimidazole-linked polymer membranes that display an unprecedented H2/CO2 selectivity (up to 40) at 423 K together with high-pressure resistance and long-term stability (>800 hours in the presence of water vapor).