The system under study is a twin-layered lattice gas at half filling, being driven to nonequilibrium steady states by a large, finite "electric" field. By making intralayer couplings unequal, we were able to extend the phase diagram obtained by Hill, Zia, and Schmittmann and found some interesting effects. Many transient phases to the strip phase were found to be long lived. We also attempted to test whether the driven lattice gas with negative interlayer coupling is still in the Ising universality class. Simulation results suggest a value of 1.75 for the exponent gamma but a value closer to 2.0 for the ratio gamma/nu. We suspect a different susceptibility has to be used due to the presence of two phases near criticality.