A re-writable resistance-switching memory cell includes first and second capacitors in series. The first and second capacitors may have balanced electrical characteristics to allow nearly concurrent, same-direction switching. The first capacitor has a first bipolar resistance switching layer between first and second conductive layers, and the second capacitor has a second bipolar resistance switching layer between third and fourth conductive layers. The first and third conductive layers are made of a common material, and the second and fourth conductive layers are made of a common material. In one approach, the first and second bipolar resistance switching layers are made of a common material and have common thickness. In another approach, the first and second bipolar resistance switching layers are made of materials having different dielectric constants, but their thickness differs in proportion to the difference in the dielectric constants, to provide a common capacitance per unit area.