We apply a modified mean-field density functional theory to determine the phase behavior of binary mixtures of Stockmayer fluids whose spherical constituents interact according to Lennard-Jones (LJ) pair potentials with embedded pointlike dipole moments. On the basis of systematic numerical calculations we construct the global phase diagrams of these systems in the three-dimensional thermodynamic space of temperature, pressure, and chemical potential difference of the two components. The vapor-liquid, isotropic liquid -isotropic liquid, isotropic liquid -ferromagnetic liquid, and ferromagnetic liquid -ferromagnetic liquid first-order phase separations are investigated. The loci of the second-order isotropic fluid -ferromagnetic fluid transition are calculated from Landau theory. Liquid-vapor and liquid-liquid critical lines, tricritical lines, triple lines, and lines of critical end points of the binary Stockmayer mixtures are also determined. We discuss how the topology of the phase diagrams change upon varying the strengths of the two dipole moments of the two species as well as their sizes.