Using Brownian-Dynamics simulations, a two-dimensional mixture of charged soft spheres is considered as a model system for cat-anionic lipid layers in tangential electric fields. Electrophoretic mobilities and diffusion constants are determined for a wide range of densities, electric field and Coulomb coupling strengths; the experimentally discovered violation of the Nernst-Einstein relation is reproduced for elevated densities. At large driving fields, a non-equilibrium transition into a charge-modulated structure (at finite Coulomb interaction between particles) or a macroscopic phase separation (at vanishing Coulomb coupling) is found, which might be experimentally reached with mixtures of rather incompatible cationic and anionic lipids.