The sustainable development of highly efficient industrial technologies involving membrane processes requires the creation of “next generation” polymer-based membrane materials. An important aspect of this study is the selection of synthetic titanosilicate minerals with a zeolite-like crystalline structure as fillers for modifying a polymer matrix. The developed novel dense film membranes are based on P84 copolyimide (coPI) containing 20 wt% of synthetic titanosilicate minerals: lintisite (AM-4) or natisite. The structural features of the prepared dense films were studied by wide-angle X-ray diffraction, scanning electron microscopy, and atomic force microscopy. The influence of titanosilicate minerals on the copolyimide characteristics was evaluated using physical and mechanical methods and membrane technique. The transport properties of films were studied in the separation of water/isopropanol mixtures by pervaporation. All film samples were water-selective. The introduction of 20 wt% titanosilicate minerals into the coPI matrix resulted in enhanced separation efficiency of copolyimide membranes. This enhancement is attributed to high hydrophilicity and density of the coPI/natisite film. The obtained coPI/natisite composite can be used to solve the important problem of separating the azeotropic isopropanol/water (12%) mixture, since the pervaporation separation index of this membrane is more than three times higher than that of the pristine coPI film.