Asymmetric membrane materials based on MK-40 membranes modified with a thin layer of perfluorinated ion exchangers MF-4SK with embedded polyaniline were obtained. The diffusion characteristics of the obtained composites are investigated. An abnormal asymmetry of ion transport in a neutral medium was detected. The diffusion coefficients of individual cations for membranes with mixed cation composition were estimated. The conductivity of composites was investigated. The activation energies are estimated. It was shown that the maximum ionic conductivity is observed for membranes with a 2% polyaniline content, which is consistent with the theory of limited membrane pore elasticity.