We report a detailed account of the phase diagram of a recently introduced model for nonequilibrium wetting in (1+1) dimensions [H. Hinrichsen, R. Livi, D. Mukamel, and A. Politi, Phys. Rev. Lett. 79, 2710 (1997)]. A mean-field approximation is shown to reproduce the main features of the phase diagram, while providing indications for the behavior of the wetting transition in higher dimensions. The mean-field phase diagram is found to exhibit an extra transition line which does not exist in (1+1) dimensions. The line separates a phase in which the interface height distribution decays exponentially at large heights from a superexponentially decaying phase. Implications to wetting in dimensions higher than (1+1) are discussed.