We use tunneling spectroscopy in Al and Nb based superconductor-insulator-superconductor (SIS) junctions to demonstrate the existence of metallic quasiparticle states at the interface of a superconducting electrode and an oxide layer, introducing a new method to directly evaluate the interface quasiparticle areal density of states. Current-voltage (I-V) characteristics typically observed in metal-insulator-superconductor (MIS) junctions are observed in the subgap voltage region. The turn-on voltage of the MIS-type leakage is found to be determined by the superconducting electrode with a smaller gap energy (Delta), and its magnitude depends on the nature of the interface. Our experiment suggests that the interface plays a key role in contributing to the subgap leakage influencing the performance of superconducting circuits.