We have studied several non-equilibrium lattice gases with particle-co
nserving dynamics. The lattice consists of two planes, and particles i
nteract (attract) only with nearest-neighbour particles within the sam
e plane but may hop to the other. In addition to the standard heat bat
h at temperature T, a mechanism exists that biases a principal axis, n
amely, we assume either that particles are also driven by a constant f
ield, or else that exchanges along the given axis occur completely at
random as governed by an additional heat bath at infinite temperature.
Kinetic mean-field theory and high-temperature series expansions reve
al some interesting properties of steady states which we compare with
the case of the plane. In particular, the system exhibits at T' the st
rong phase transition reported for driven gases, and also phase segreg
ation below T < T' whose nature varies with a dynamical rule.