The synthesis of a polymer that combines the processability of plastics with the extreme rigidity of cross-linked organic networks is highly attractive for molecular sieving applications. However, cross-linked networks are typically insoluble or infusible, preventing them from being processed as plastics. Here, we report a solution-processable conjugated microporous thermoset with permanent pores of ~0.4 nm, prepared by a simple heating process. When employed as a two-dimensional molecular sieving membrane for hydrogen separation, the membrane exhibits ultrahigh permeability with good selectivity for H2 over CO2, O2, N2, CH4, C3H6 and C3H8. The combined processability, structural rigidity and easy feasibility make this polymeric membrane promising for large-scale hydrogen separations of commercial and environmental relevance.