Asymmetric membrane materials based on MC-40 membranes modified with a thin layer of MF-4SC perfluorinated ion exchangers with introduced polyaniline were obtained. The diffusion parameters of the resulting composites were studied. The anomalous asymmetry of ion transport in neutral solution was found. The diffusion coefficients of individual cations in the membranes with mixed cationic compositions were estimated. The conductivity of the composites was studied. The activation energies were evaluated. It was found that the membranes containing 2% polyaniline exhibited a maximum ionic conductivity, which is consistent with a model of the limited elasticity of membrane pores.