Bipolar resistive switching in metal-insulator-metal structures based on a double-layer insulator composed of a layer of yttria-stabilized zirconia (YSZ) containing 12 mol % Y2O3 and a layer of GeOx is studied. It is shown that the incorporation of an additional GeOx layer into the structure leads to a significant decrease in the variation of resistive switching parameters at both negative and positive voltages. Au/Zr/GeOx/YSZ/TiN structures exhibit a high stability of the resistance ratio in high-resistance and low-resistance states during cyclic switching. The studied structures can be used for designing next-generation nonvolatile memory elements.