In a continuing study on the properties of the compressible lattice model, the equation of state and miscibility behavior of binary mixtures of lattice chains is explored. Monte Carlo simulations are performed in the NpT and semi-grand-canonical mu pT ensemble for varying compositions and several combinations of the three interactional parameters characterizing the binary mixture. In all simulations the chain lengths of both components are taken to be equal. In addition to the thermodynamic information, microscopic information on the number of different contacts and the mean square end-to-end distance is collected, too. The Monte Carlo results are used to examine the predictions of lattice model theories derived from statistical mechanics. To this purpose the nonrandom mixing theory for the binary compressible mixture, based on the quasi-chemical approximation of Guggenheim, is presented. The theory is compared in detail to the collected simulation data. Although the theory is completely general, the comparison is limited, by the simulation data, to symmetric chain lengths. Furthermore, the relation of this theory to other frequently used approximate theories is explained. It is shown that the nonrandom mixing theory gives the best agreement with simulation data. Nevertheless, for the miscibility behavior and the number of contacts in particular, deviations remain that are related to neglect of the excluded volume of the chain molecules and critical phenomena.