Two homometallic class-I dinuclear mixed valence cobalt complexes, [(N3)CoIIIL1(μ-C6H4(NO2)CO2)CoII(N3)] (1) and [(N3)CoIIIL2(μ-C6H4(NO2)CO2)CoII(N3)] (2), have been synthesized using multisite N2O4 coordination ligands, H2L1 {where H2L1 = (2,2-dimethyl-1,3-propanediyl)bis(iminomethylene)bis(6-methoxyphenol) and H2L2 = (2,2-dimethyl-1,3-propanediyl)bis(iminomethylene)bis(6-ethoxyphenol)}. Each complex has been structurally characterized by single crystal X-ray diffraction and spectral analysis. Both the cobalt centers in these dinuclear complexes adopt a distorted-octahedral geometry, where the cobalt(iii) center resides at the inner N2O2 cavity and the cobalt(ii) center resides at the outer O4 cavity of the reduced Schiff base. Both of them show good electrical conductivity, which has been rationalized by band gap measurements. The band gap in the solid state has been determined by experimental and DFT calculations and it confirms that each of the two complexes behaves as a semiconductor. The space-charge-limited current (SCLC) theory is employed to evaluate the charge transport parameters such as effective carrier mobility and transit time for both complexes. The difference in the conductivity values of the complexes may be correlated with the strengths of extended supramolecular interactions in the complexes. Bader's quantum theory of atoms-in-molecules (QTAIM) is applied extensively to get quantitative and qualitative insights into the physical nature of weak non-covalent interactions. In addition, the non-covalent interaction reduced density gradient (NCI-RDG) methods well support the presence of such non-covalent intermolecular interactions.