Electronic and structural detail at the electrode-molecule interface have a significant influence on charge transport across molecular junctions. Despite the decisive role of the metal-molecule interface, a complete electronic and structural characterization of the interface remains a challenge. This is in no small part due to current experimental limitations. Here, we present a comprehensive approach to obtain a detailed description of the metal-molecule interface in single-molecule junctions, based on current-voltage (I-V) measurements. Contrary to conventional conductance studies, this I-V approach provides a correlated statistical description of both, the degree of electronic coupling across the metal-molecule interface, and the energy alignment between the conduction orbital and the Fermi level of the electrode. This exhaustive statistical approach was employed to study single-molecule junctions of 1,4-benzenediamine (BDA), 1,4-butanediamine (C4DA), and 1,4-benzenedithiol (BDT). A single interfacial configuration was observed for both BDA and C4DA junctions, while three different interfacial arrangements were resolved for BDT. This multiplicity is due to different molecular adsorption sites on the Au surface namely on-top, hollow, and bridge. Furthermore, C4DA junctions present a fluctuating I-V curve arising from the greater conformational freedom of the saturated alkyl chain, in sharp contrast with the rigid aromatic backbone of both BDA and BDT.