The phase behavior and global phase diagram of binary mixtures of attractive hard spheres described by a hard-sphere mixture equation of state with a mean field term and the Lorentz-Berthelot combining rule are examined in detail in dependence on the ratio of (i) the hard-sphere diameters and (ii) the strength of the mean field attraction. It is shown that in addition to the usual phenomena, the studied mixture exhibits also the closed liquid-liquid immiscibility loop (Type VI and VII behavior) and a variety of new azeotropic phenomena. Topology of phase diagrams is discussed in detail with emphasis on the boundary states and is compared with that based on the one-fluid van der Waals equation approach.