Coated membranes comprise a porous desiccant-loaded polymer substrate that is coated on one surface with a thin layer of water permeable polymer. Such membranes are particularly suitable for use in enthalpy exchangers and other applications involving exchange of moisture and optionally heat between gas streams with little or no mixing of the gas streams through the membrane. Such membranes have favorable heat and humidity transfer properties, have suitable mechanical properties, are resistant to the crossover of gases when the membranes are either wet or dry, and are generally low cost.