This manuscript examines the transport of H2O, H-2 and O-2 through membranes, which conduct protons (H+), oxygen ions (O-2) and holes (h(.)). Transport equations are derived under the assumption of steady state and fast surface kinetics. The specific cases considered hen include the transport of H2O and O-2 through membranes in H2O-O-2 gaseous mixtures, and the transport of H2O and H-2 in H2O-H-2 gaseous mixtures. The transport equations show that Onsager cross coefficients are symmetric, as required. Permeation of H2O, H-2, and O-2 through single phase, two-phase and multiphase composite membranes is discussed. The analysis shows that the transport of neutral species, namely H-2, O-2, and H2O, can occur up their chemical potential gradients through the existence of cross terms.