Biological applications involving membrane problems on different scales are numerous. We propose an extension of the standard Turing theory to the case of two domains separated by a permeable membrane. To this aim, we study a reaction-diffusion system with zero-flux boundary conditions on the external boundary and Kedem-Katchalsky membrane conditions on the inner membrane. We use the same approach as in the standard Turing theory, but applied to membrane operators. New constraints have to be added, due to the presence of permeability coefficients. Finally, we perform an explicit one dimensional analysis, combined with numerical simulations, to validate the theoretical results. The case of a fast reaction-diffusion system is also considered.