The processes taking place in the CuI/L/solv system (L = bipy, phen) in the presence of the [B12H12]2– anion, which exhibited the lowest reducing ability among the [BnHn]2– cluster anions (n = 6, 10, 12), were studied. The binuclear complexes [Cu2(L)4(μ-CO3)][B12H12] · n(solv) were found to be formed upon the redox reaction of (C6H5)4P[Cu[B12H12]] with a twofold excess of L or the reaction of copper(II) complex [(Cu2(phen)4(CO3)]Cl2 with [(C4H9)3NH]2[B12H12]. The Cu(II) complexes were characterized by X-ray diffraction; their EPR-spectra were studied at 295 K and the magnetic measurements were performed in the 300–2 K range. In the [Cu2(phen)4(μ-CO3)][B12H12] · DMF dimer with the anti-anti coordination of the (μ-CO3)-group, strong antiferromagnetic interactions occur between the Cu(II) atoms (Cu⋯Cu = 5.107 Å).