A gas of interacting surfaces with energy depending on area and mean curvature is described as an Ising spin model on a cubic lattice. The interfacial properties in the region where the nearly pure ordered phases and the high-temperature disordered phase coexist are studied. On the coexistence line we find in mean-field approximation a first-order wetting transition whose position varies between the tricritical point and a 4-phase point, depending on the parameters of the model. For some range of the parameters the structured region of the high-temperature phase wets the nearly pure phases interface.