The development of reliable redox-based resistive random-access memory devices requires understanding and disentangling concurrent effects present at memristive interfaces. We report on the fabrication and electrical characterization of TiO_x/La_1/3Ca_2/3MnO_3-x microstructured interfaces and on the modeling of their memristive behavior. We show that a careful tuning of the applied external electrical stimuli allows controlling the redox process between both layers, obtaining multilevel non-volatile resistance states. We simulate the oxygen vacancies dynamics at the interface between both oxides, and successfully reproduce the experimental electrical behavior after the inclusion of an electronic effect, related to the presence of an n-p diode at the interface. The formation of the diode is due to the n- and p-character of TiO_x and La_1/3Ca_2/3MnO_3-x, respectively. Our analysis indicates that oxygen vacancies migration between both layers is triggered after the diode is polarized either in forward mode or in reverse mode above breakdown. Electrical measurements at different temperatures suggest that the diode can be characterized as Zener-type. The advantages of our junctions for their implementation in RRAM devices are finally discussed.