Using computer simulations, we have investigated the kinetics of a two-dimensional, two-component fluid mixture on a lattice in the presence of a field which drives the different species in opposite directions. A kinetic instability arises when the field strength and fluid density are sufficiently large. The nonuniform state which emerges has zero flux and consists of layers of particles, essentially close-packed and perpendicular to the field direction. The layers each contain particles of essentially a single species, but the layer composition alternates between the different species with periodicity depending on the fluid density and the field strength. A mean-field analysis suggests this is a first-order dynamic phase transition, which is consistent with the computer simulations.