The four new complexes, [Cu(HL1)(L2)Cl] (1), [Cu(HL1)(L1)]∙Cl∙2H2O (2), [Co(L1)2]∙Cl (3) and [Cd(HL1)I2]∙dmso (4), have been prepared by one-pot reactions of the respective chloride or iodide metal salt with a non-aqueous solution of the polydentate Schiff base, HL1, resulted from in situ condensation of benzhydrazide and 2-pyridinecarboxaldehyde, while a ligand HL2, in case of 1, has been formed due to the oxidation of 2-pyridinecarboxaldehyde under reaction conditions. The crystallographic analysis revealed that the molecular building units in 1-4 are linked together into complex structures by hydrogen bonding, resulting in 1D, 2D and 3D supramolecular architectures for 1, 2 and 4, respectively, and the supramolecular trimer for 3. The electronic structures of 1-4 were investigated by the DFT theoretical calculations. The non-covalent interactions in the crystal structures of 1-4 were studied by means of the Hirshfeld surface analysis and the QTAIM theory with a special focus on the C-H⋯Cl bonding. From the DFT/DLPNO-CCSD(T) calculations, using a series of charged model {R3C-H}0⋯Cl- assemblies, we propose linear regressions for assessment of the interaction enthalpy (ΔH, kcal mol-1) and the binding energy (BE, kcal mol-1) between {R3C-H}0 and Cl- sites starting from the electron density at the bond critical point (ρ(rBCP), a.u.): ΔH = -678 × ρ(r) + 3 and BE = -726 × ρ(r) + 4. It was also has been found that compounds 1, 3 and 4 during in vitro screening showed an antibacterial activity toward the nine bacteria species, comprising both Gram-positive and Gram-negative, with MIC values ranging from 156.2 to 625 mg/L. The best results have been obtained against Acinetobacter baumannii MβL.