An experimental protocol of preparation of homogeneous and nanocomposite chitosan (Ch) based membranes supported on polyamide-6 (PA6) films was developed and described in detail. Montmorillonite (MMT) and Cloisite 30B (C30B) nanoclays were used as nanofillers to improve mechanical properties of chitosan films. The surface, mechanical, and transport properties of PA6 supported Ch, Ch/MMT and Ch/C30B membranes were studied and compared with a pristine, non-supported chitosan membrane. Implementation of advanced analytical techniques e.g., SEM reveal the clays nanoparticles are well dispersed in the chitosan matrix. According to AFM images, composite chitosan/nanoclay membranes possess higher roughness compared with unfilled ones. On the other hand, an incorporation of clay particles insignificantly changed the mechanical and thermal properties of the membranes. It was also found that all membranes are hydrophilic and water is preferentially removed from EtOH/H2O and iPrOH/H2O mixtures by pervaporation. Supporting of chitosan and chitosan/nanoclay thin films onto PA6 porous substrate enhanced permeate flux and pervaporation separation index, in comparison to the pristine Ch membrane. Concerning separation factor (β), the highest value equal to 4500 has been found for a chitosan composite membrane containing Cloisite 30B contacting 85/15 wt % iPrOH/H2O mixture. The mentioned membrane was characterized by the normalized flux of 0.5 μm kg m−2 h−1. Based on the established data, it was possible to conclude that chitosan membranes are meaningful material in dehydration of azeotropic mixtures. Nevertheless, to boost up the membrane efficiency, the further modification process is required.