A Gibbs ensemble algorithm implemented previously for mixtures of homopolymers and copolymers in a cubic lattice with coordination number z=26 is now used to characterize the complete phase separation diagram of the ternary mixtures formed by AA and BB homopolymers and their common symmetric diblock copolymer AB, all chains of the same length. We consider two alternative types of systems with repulsions between neighboring A and B units or with attractions between A and A or B and B neighboring units. A certain proportion of voids is included in both cases. The 3-phase region of the diagram is obtained by using a 3-box algorithm that has not been previously employed for polymer mixtures. The 3-phase region is composed of two homopolymer-rich asymmetric phases, each one mainly composed of a different homopolymer component together with a small proportion of copolymer. These two phases are in equilibrium with a third phase rich in copolymer. The 3-phase region connects smoothly with the 2-phase region covered by our 2-box simulations reported earlier for low copolymer composition. Similarly, it also connects with two asymmetric 2-phase regions characterized now through 2-box simulations performed with a low initial proportion of one of the homopolymer components. The data obtained for the systems with repulsions are in agreement with earlier single box Monte Carlo estimations for ternary mixtures with a symmetric homopolymer composition. They show a non-clearly structured copolymer-rich phase with a substantial amount of homopolymer, while the presence of copolymer in the AA or BB enriched phases is small. The systems with attractions, however, exhibit important differences with respect to this picture, due to a more specific role of the voids. Some differences with respect to the mean-field theory predictions are also discussed. (C) 2003 American Institute of Physics.