Electronic-structure calculations allow us to predict that hypothetical ordered mixed crystals of c-BN and diamond representative of the expected short-range order in the alloys show a very pronounced band-gap bowing. This anomalous behavior is believed to be related to the staggered band lineup at the corresponding heterojunction. The miscibility phase diagram of this system is estimated using a simple pseudobinary ``regular-solution'' model for the short-range order and energies of formation of the representative ordered compounds calculated from first principles. It indicates that there is only very limited mutual solubility in the solid state. The band gaps and energies of formation of the disordered ternary alloys are estimated by means of cluster expansions.