A new approximate nonrandom lattice fluid model was derived and applied to pure fluids in the previous paper[You et al., 1993a], in which an explicit expression for thermodynamic properties were obtained by expanding Helmholtz free energy and the nonrandomness factor around the reference athermal solution. In this work, the model was extended tb mixtures and applied to density, to equilibria of vapor-liquid, vapor-solid and liquid-liquid phases, to multiphase equilibria including UCST behaviors, and to heat of mixing for nonpolar/nonpolar, nonpolar/polar, and polar/polar binary mixtures of simple and complex molecules. With two parameters for pure components and one binary interaction energy parameter, results obtained to date demonstrated that the mixture theory is quantitatively applicable to a wide range of temperature, pressure and density.