Two novel copper(II) heteroleptic coordination polymers {[Cu3L4](ClO4)2}n⋅nEtOH⋅11nH2O (1⋅nEtOH⋅11nH2O) and {[Cu(HL’)(SCN)]ClO4}n·nH2O (2·nH2O) were obtained from the previously unknown N’-isonicotinoylpyrazine-2-carbohydrazonamide (HL) and Cu(ClO4)2 or a mixture of Cu(ClO4)2 and KSCN, respectively, in aqueous ethanol. The parent organic ligand is involved in its deprotonated form L in the former complex, while in the latter complex, the parent ligand HL transforms into its zwitterionic form HL’, where the amide nitrogen atom is negatively charged, and the pyridine fragment is protonated. A crucial role of the additional auxiliary ligand (SCN–) was revealed as a driving force for the formation of the resulting dense supramolecular architecture 2·nH2O in comparison to the porous complex 1⋅nEtOH⋅11nH2O. Complex 1⋅nEtOH⋅11nH2O exhibits a structure with the polymeric {[Cu3L4]n}2n+ cation counterbalanced by the ClO4– anions. The polymeric cation is constructed from two types of coordination nodes, one of which is produced from the Cu2+ cation, N,N’,O-chelated by two anionic ligands L, while the second node is fabricated from the other Cu2+ cation, N,N’,O-chelated by one anionic ligand L and by two pyridine fragments of the other two ligands L. Thus, the metal cations in the structure of the polymeric {[Cu3L4]n}2n+ cation are in distorted octahedral N4O2 and distorted square-pyramidal N4O coordination environments. Complex 2·nH2O exhibits a structure with the polymeric heteroleptic {[Cu(HL’)(SCN)]n}n+ cation counterbalanced by the ClO4– anions. The polymeric cation is constructed from the [Cu(HL’)(SCN)(NCS)] coordination nodes. The HL’ ligand also exhibits the same N,N’,O-chelating mode and the metal cations in the structure of the polymeric {[Cu(HL’)(SCN)]n}n+ cation are in a square-pyramidal N3OS coordination environment. For the latter compound, DFT analysis was conducted to elucidate the nature of the apical Cu···SCN coordination bond, which can also be interpreted as a Cu···S noncovalent regium bond. This compound can be formulated as a discrete ion-pair with the Cu metal center adopting a square planar coordination, [Cu(HL’)(SCN)]ClO4. The monomers are propagated by a combination of regium bonding and anion···π interactions, further assisted by S···O chalcogen bonds. Finally, both coordination polymers are the first examples of the HL-derived metallocomplexes. Thus, in the present work we introduce a new polydentate compound HL, which is of potential importance as a building unit for the coordination chemistry.