We have calculated the energies of mixing of the rock salt structure solid solutions MnO-NiO, MgO-MnO, and CaO-MnO using periodic ab initio Hartree-Fock Hamiltonians; a posteriori corrections for electron correlation derived from density-functional theory have also been evaluated. The agreement of the correlation-corrected values with available experimental data is very good. Magnetic interactions in the solid are reproduced correctly, but their neglect does not influence strongly the calculated mixing energy. Atomic relaxation, however, has an important effect on the calculated energetics. Comparing the electronic distribution in the pure oxides and the solid solutions, we find neither induced spin polarization on the oxygen ions nor electronic relaxation in the three mixed systems. Additionally, we performed atomistic lattice simulations based on interatomic potentials, which in the case of the MnO-NiO and CaO-MnO solid solutions predict energies of mixing that are significantly high compared with experiment. By fitting to our ab initio data we derived a new set of potentials, which reproduce experimental results more accurately. Finally, we calculated the temperature dependence of the energy of mixing for MgO-MnO by performing Gibbs free energy minimizations at different temperatures up to 1000 K. The results indicate a negligible temperature dependence of the calculated energies of mixing.