The present invention discloses polymer functionalized molecular sieve/polymer mixed matrix membranes (MMMs) with either no macrovoids or voids of less than several Angstroms at the interface of the polymer matrix and the molecular sieves by incorporating polyethersulfone (PES) or cellulose triacetate (CTA) functionalized molecular sieves into a continuous polyimide or cellulose acetate (CA) polymer matrix. The MMMs, in the form of symmetric dense film, asymmetric flat sheet membrane, or asymmetric hollow fiber have good flexibility and high mechanical strength, and exhibit significantly enhanced selectivity and/or permeability over the polymer membranes made from the corresponding continuous polymer matrices for carbon dioxide/methane (CO2/CH4) and hydrogen/methane (H2/CH4) separations. The MMMs are suitable for a variety of liquid, gas, and vapor separations such as deep desulfurization of gasoline and diesel fuels, ethanol/water separations, pervaporation dehydration of aqueous/organic mixtures, CO2/CH4, CO2/N2, H2/CH4, O2/N2, olefin/paraffin, iso/normal paraffins separations, and other light gas mixture separations.