The "acidic mantle" of the skin surface has been related to several essential functions of the skin. although the origin of the acidity is still obscure. In this paper, we investigate how different transport processes can influence the lcocal proton concentration inside a membrane consisting of oriented lipid bilayers. This system is chosen as a simple model of the extracellular lipids in the upper layer of the skin, the stratum corneum. We present a theoretical model for diffusional transport over the membrane in the presence of an osmotic gradient and a gradient in CO2, taking into account the influence of these gradients on the lipid structure and the local electrostatics. We are also discussing the complications in applying the concept of pH to the stratum corneum. From this, we make the following conclusions: (i) The definition of pH in the stratum corneum is ambiguous, and thus, all statements regarding pH should always be related to a clear definition. (ii) A natural definition of pH in the stratum corneum can be proposed which takes into account local heterogeneity, local charges, and the fact that the stratum corneum is not in thermodynamical equilibrium. (iii) Diffusive transport across an oriented bilayer stack in the presence of an osmotic gradient and/or a gradient in CO2 can give rise to a substantial gradient in pH. (iv) The results from the simplified model can be correlated to experimental observations of pH in the stratum corneum.