  We study the steady state of a phase-separated driven Ising lattice gas in
three dimensions using computer simulations with Kawasaki dynamics. An external
force field F(z) acts in the x direction parallel to the interface, creating a
lateral order parameter current j^x(z) which varies with distance z from the
interface. Above the roughening temperature, our data for `shear-like' linear
variation of F(z) are in agreement with the picture wherein shear acts as
effective confinement in this system, thus supressing the interfacial
capillary-wave fluctuations. We find sharper magnetisation profiles and reduced
interfacial width as compared to equilibrium. Pair correlations are more
suppressed in the vorticity direction y than in the driving direction; the
opposite holds for the structure factor. Lateral transport of capillary waves
occurs for those forms of F(z) for which the current j^x(z) is an odd function
of z, for example the shear-like drive, and a `step-like' driving field. For a
V-shaped driving force no such motion occurs, but capillary waves are
suppressed more strongly than for the shear-like drive. These findings are in
agreement with our previous simulation studies in two dimensions. Near and
below the (equilibrium) roughening temperature the effective-confinement
picture ceases to work, but the lateral motion of the interface persists.
