The present invention discloses composite inorganic membranes, methods for making the same, and methods of separating gases, vapors, and liquids using the same. The composite zeolite membrane is prepared by TS-1 zeolite membrane synthesis, and subsequent palladium doping. In the composite zeolite membrane synthesis, two different methods can be employed, including in-situ crystallization of one or more layers of zeolite crystals an a porous membrane substrate, and a second growth method by in-situ crystallization of a continuous second layer of zeolite crystals on a seed layer of MFI zeolite crystals supported on a porous membrane substrate. The membranes in the form of disks, tubes, or hollow fibers have high gas selectivity over other small gases, very good impurity resistance, and excellent thermal and chemical stability over polymer membranes and other inorganic membranes for gas, vapor, and liquid, separations.