The fundamental dimensionless groups for coupled heat and moisture transfer in a cross how air-to-air enthalpy exchanger with hydrophilic membrane cores are derived and validated with experimental data. The thermal and moisture transfer mechanisms in membranes are studied. The finite difference numerical solutions of the model are used to study heat and moisture transfer in enthalpy exchangers. The variations of sensible, latent, and enthalpy effectiveness with various operating parameters are calculated for different types of material. Studies show that the sensible effectiveness is mainly determined by number of transfer units (NTU) of the exchanger, while the latent effectiveness is influenced by both the material and the operating conditions. Unlike thermal diffusive resistance, the moisture diffusive resistance in membrane is not a constant. It is co-determined by the slopes of sorption curves and the operating conditions. To account for these influences, a new dimensionless factor named the coefficient of moisture diffusive resistance (CMDR) is defined. With this coefficient, the performance of an enthalpy exchanger can be more easily predicted and clearly understood. By comparing the performances with different membrane materials, it is revealed that the membrane material with a linear sorption curve performs better than other materials under common conditions.