In this paper we examine the problem of diffusion and reaction in biofilms and cellular systems when the reaction rate is limited by both a substrate and an electron acceptor. The intercellular kinetics is represented by a conventional multiplicative expression for the reaction between the substrate and oxygen, and by a first-order endogenous respiration rate. The membrane transport process for substrate and oxygen occurs through two different mechanisms. The transport of the electron acceptor is described by a permeability model while the transport of the substrate is treated in terms of a simple carrier model. The microscopic (sub-cellular) description is used to develop an upscaled version of diffusion and reaction in biofilms and other cellular media. The effective diffusivity that appears in the macroscopic description is predicted by a closure problem. Solutions to this closure problem are presented for simplified geometries, and the effective diffusivity predicted by the theory is compared with experimental values.