We extend our previous treatment of a mixed ionic electronic conductor membrane, consisting of a porous cathode and anode separated by a thin non-porous layer, to the case where mass transport of molecules in the porous electrodes can be the rate-limiting step. The linearized transport equations for the ion-hole pairs in the solid and of the gas molecules in the pores are characterized by the length scales L(p) = root L(d)(1-phi)/S tau(s) and L(g) = 2L(p) root[tau(s) phi/tau(1-phi)][D(g)c(g)/D(IE)c(i)] respectively, where L(d) = D-IE/K is the length scale that determines the transition from diffusion limited to surface exchange limited transport in the non-porous electrodes, K is the surface exchange coefficient, D-IE and D-g are the diffusion coefficients of the ion-hole pairs and of the molecules, c(i) and c(g) are the concentrations of the ions and molecules, S is the pore surface area per unit volume, phi the porosity and tau(s) and tau the tortuosities of the solid and pore phases respectively. When L(g) much greater than L(p), which is the case treated previously, the rate-limiting step in the transport is ionic diffusion and surface exchange. Enhancements in oxygen ion current of two orders in magnitude, over non-porous electrodes, are in principle achievable with porous perovskite MIEC having surface area S = 10(6) cm(-1). When L(g) much less than L(p) the rate-limiting step is mass transport in the pores and the enhancement in ion current is substantially reduced.