The statistical associating fluid theory of Wertheim is applied to describe binary mixtures with associating between unlike-pair molecules. The phase behavior of this binary mixture would fall into five different types (I, II, III, V, and VI) of the classification scheme of van Konynenburg and Scott by varying the associating strength and the energy parameters. Both interfacial wetting behavior and wetting transitions are carefully examined in all the vapor-liquid-liquid (gamma-beta-alpha) three-phase-coexisting regions of the binary mixtures. The global wetting behavior and wetting transitions are delineated by scanning the parameter space. In certain regions, the middle 0 phase exhibits interfacial phase transitions sequentially, nonwetting -> partial-wetting -> nonwetting, at the interface separating lower alpha and upper gamma phases along with increasing temperature.