We report the experimental investigation of bipolar resistive switching with "table with legs" shaped hysteresis switching loops in epitaxial perovskite GdBaCo2O5+delta/LaNiO3 bilayers deposited by pulsed laser deposition. The possibility of varying the resistivity of GdBaCo2O5+delta by changing its oxygen content allowed engineering this perovskite heterostructure with controlled interfaces creating two symmetric junctions. It has been proved that the resistance state of the device can be reproducibly varied by both continuous voltage sweeps and by electrical pulses. The symmetric devices show slightly non-symmetric resistance profiles, which can be explained by a valence change resistive switching model, and presented promising multilevel properties required for novel memories and neuromorphic computing.