Membrane technology has become increasingly important as a separation technology. In current modelling on mass and heat transport processes in a membrane system the common assumption is to take the relevant transport variables, such as temperature or chemical potential, as continuous functions at the membrane boundaries. One aim of this chapter is to present a more detailed examination of the membrane function if this equilibrium assumption is removed. In addition, it has been documented in the literature on membrane transport processes that thermodynamic coupling exists between thermal and diffusion fluxes. Coupling means that a mass flux can be originated by a temperature difference, and that a heat flux can be caused by a chemical-potential difference alone. The other aim of this chapter is to describe systematically these reciprocal effects by using the theory of non-equilibrium thermodynamics.