We report on the fabrication and characterization of metal/insulator/metal capacitor like devices, with both rectifying and hysteretic features. Devices are formed by two junctions, Ti/HfO₂ and Co/HfO₂. Each junction exhibits highly repetitive hysteretic I-V curves with a sharp transition from a high to a low resistance state (3-4 orders of magnitude jump). The opposite transition (from low to high) is induced by polarity reversal. The rectifying non-crossing characteristics of the I-V branches denote their potential use as a multifunctional device, acting as a built-in rectifier and memory cell in a single device. Based on the phenomenological model description by Zazpe et al. [Appl. Phys. Lett. 103, 073114 (2013)], we propose a circuital equivalent representation supported on switchable rectifying junctions. By exploring different electrode connections, we disentangle the role of the bulk transport in HfO₂ devices.