The Nernst-Planck-Smoluchowski equations of electrodiffusion are combined with the Maxwell equations on the quasistatic level in order to study a phenomenological model of electrodynamics, which takes into account the interplay between electric forces and "diffusion forces" in a more detailed fashion than in the Maxwell-Wagner-Sillars (MWS) theories of impedance and complex permittivity of heterogeneous media. The general form of the linearized equations for time periodic perturbations are discussed, and the equations are solved for the perturbations of the electric charge density, the electric field strength, the electric potential, the galvanic current, and the total current in the special case, where all ions in the same phase have the same diffusion coefficient, and where all equilibrium electric double layers are linearizable. The excess interfacial impedance due to the dynamic double layers near the interface are calculated apart from an arbitrary constant. To determine this constant is complicated, when the ions at phase contact distribute themselves according to different Nernst distribution coefficients, but in the case of equal distribution coefficients for all ions, a simple analytical expression is obtained for the excess impedance for an interface between two semi-infinite phases. "Excess" means "in excess of the Maxwell-Wagner-Sillars impedance." The expressions are also valid for lamellar membranes with nonoverlapping dynamic, electric double layers ("thick layer, lamellar membranes"). A model "cellulose acetate membrane" is investigated as an example. The models proposed are well suited to discuss the limitations of the usual Maxwell-Wagner-Sillars treatment of the impedance or the dielectric dispersion of heterogeneous media based on the so-called "principle of generalized conductivity." The MWS theory may lead to erroneous analysis, especially in the case of measurement of the complex permittivity.