The invention discloses the use of 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, particularly PES functionalized AlPO-14/polyimide MMMs and CTA functionalized AlPO-14/CA 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), hydrogen/methane (H2/CH4), propylene/propane separations and a variety of liquid, gas, and vapor separations.