Three novel heterometallic Ni/Cd coordination compounds [Ni(en)3][CdCl4]∙3dmso (1), [Ni(en)2(dmf)2][CdBr4] (2), and [Ni(en)3]2[CdI4](I)2 (3) have been synthesized through the self-assembly process in a one-pot reaction of cadmium oxide, nickel salt (or nickel powder), NH4X (X = Cl, Br, I), and ethylenediamine in non-aqueous solvents dmso (for 1) or dmf (for 2 and 3). Formation of the one- (1) or three-dimensional (2 and 3) hydrogen-bonded frameworks has been observed depending on the nature of the [CdX4]2− counter-anion, as well as on the nature of the solvent. The electronic structures of [Ni(en)3]2+ and [Ni(en)2(dmf)2]2+ cations were studied at the DFT and CASSCF levels, including the ab initio ligand field theory (AILFT) calculations. The non-covalent intermolecular contacts between the cationic nickel and anionic cadmium blocks in the solid state were investigated by the QTAIM analysis. The mechanism of ligand substitution at the nickel center in [Ni(en)2(dmf)2]2+ was theoretically investigated at the ωB97X-D4/ma-def2-TZVP//DLPNO-CCSD(T)/ma-def2-TZVPP level. The results demonstrate that thermodynamic factors are structure-determining ones due to low energy barriers of the rotation of dmf ligands in [Ni(en)2(dmf)2]2+ (below 3 kcal mol−1) and the reversible transformation of [Ni(en)2(dmf)2]2+ into [Ni(en)3]2+ (below 20 kcal mol−1).