Poly(biquinoline dicarbohydrazide)-co-(bistrimelliteimide) methylene-bisanthranylide (PQHI) and its metal-polymer complex PQHI-Cu⁺ containing several types of functional groups (hydrazide, carboxyl, amide, and imide fragments) were synthesized. Dense thin-film membranes were prepared to study transport properties of these polymers in the separation of a benzene and isopropanol (IPA) mixture via pervaporation. Comprehensive studies of structure, physical and mechanical properties of the novel membranes were carried out. Structure of the polymer films was characterized using scanning electron microscopy. Measurements of physical and mechanical properties showed good performance capabilities of polymers as membrane materials. Transport properties of the synthesized polymers in pervaporation of benzene–IPA mixtures were characterized by determination of total flux, separation factor, as well as permeability and selectivity of the films. It was experimentally found and confirmed by quantum chemical calculations that the novel PQHI-based membranes are benzene selective due to the presence of functional groups capable of H-bonding. The benzene/IPA separation factor is equal to 38 for the PQHI membrane in pervaporation of the mixture containing 20 wt% of benzene.