We consider a mixed-spin Ising model with three-sublattices consisting of Ni (spin-1), Mn (spin-5/2) and Cr (spin-3/2) atoms. The effect of single-ion anisotropy on magnetic properties, particularly the emergence of negative magnetization, as well as thermodynamic properties such as internal energy, entropy, free energy and heat capacity have been studied theoretically under the mean field approximation. The system is modeled as two interpenetrated face centered cubic structures to simulate the geometry of the PBA-like NiIIMnII[CrIII(CN)6].nH2O structure exhibiting negative magnetization behavior and having the compensation point. One of them alternately contains Ni and Mn atoms, forming sublattices A and B respectively, while the other structure contains entirely Cr atoms and forms sublattice C. The results show that the single-ion anisotropy has significant effects on the critical temperature, compensation point and the appearance of negative magnetization. Moreover, under an external magnetic field, the system exhibits discontinuities in the magnetization curves, which are characteristic of the first-order phase transitions. These transitions also emerge in the thermodynamic quantities at the corresponding temperatures.