There is a complex interplay between the structural and other physicochemical properties of new compounds and the molecules in living organisms. To understand the mechanism of the interactions at the molecular level, the correlations between the selected properties and their biological responses have to be examined. With this aim, in this paper, density functional theory (DFT) and LMP2 calculations were carried out for the 2-acetylpyridine-aminoguanidine ligand, L, and its copper(II) complexes containing different monoanionic ligands. In addition, several parameters, most frequently used for the prediction of drug-likeness of new compounds, were calculated. The influence of the compounds on the effectiveness of the reference chemotherapeutic drug cisplatin was determined in vitro, by comparison of their combination indices (CIs). The drug interactions between cisplatin and the earlier synthesized ligands L1 (bis(3-chloropyridazine-6-hydrazone)-2,6-diacetylpyridine) and L2 (bis(phthalazine-1-hydrazone)-2,6-diacetylpyridine) and their Co(III), Ni(II), Cu(II) and Zn(II) complexes, respectively, were also measured. The ligands L, L2, and L3, as well as their complexes, showed different interactions in combination with cisplatin from strong antagonism of L to strong synergism of 4-L1 and 4-L2. The experimental results and the calculated parameters were analyzed to evaluate their correlation with the measured interactions. The thermal stability of the L·2HCl ligand and its four copper(II) complexes was determined and the thermal stability data were correlated to selected calculated molecular descriptors.