The wide possibilities of designing a chemical structure and creating complexes with transition metals make polymers of heteroaromatic structure interesting objects, from both scientific and practical aspects. In this work, modern biquinoline-containing polymers, namely polyester amide (PEA) and its metal-polymer complex (PEA-Cu(I), were synthesized and used to form dense flat membranes. A comparative study of their morphology, same physical properties (density, free volume, and contact angles), and thermomechanical characteristics was carried out. The transport properties of the modern membranes were studied during pervaporation, to solve a problem of n-heptane isolation from its binary mixtures with thiophene and methanol. It was shown that only the PEA membrane is selective for the separation of thiophene impurities from the mixture with n-heptane. In pervaporation of methanol/n-heptane mixture, the DAA-Cu(I) membrane exhibits significantly higher pervaporation separation index, as compared with that of the DAA membrane.