We have fabricated Pt/Si-rich oxide (SiO_x)/TiN stacked MIM diodes and studied an impact of the structural asymmetry on their resistive switching characteristics. XPS analyses show that a TiON interfacial layer was formed during the SiO_x deposition on TiN by RF-sputtering in an Ar + O₂ gas mixture. After the fabrication of Pt top electrodes on the SiO_x layer, and followed by an electro-forming process, distinct bi-polar type resistive switching was confirmed. For the resistive switching from high to low resistance states so called SET process, there is no need to set the current compliance. Considering higher dielectric constant of TiON than SiO_x, the interfacial TiON layer can contribute to regulate the current flow through the diode. The clockwise resistive switching, in which the reduction and oxidation (Red-Ox) reactions can occur near the TiN bottom electrode, shows lower RESET voltages and better switching endurance than the counter-clockwise switching where the Red-Ox reaction can take place near the top Pt electrode. The result implies a good repeatable nature of Red-Ox reactions at the interface between SiO_x and TiON/TiN in consideration of relatively high diffusibility of oxygen atoms through Pt.