Memory systems can include a memory device having an array of nonvolatile memory cells therein, which is electrically coupled to a plurality of bit lines and a plurality of word lines. The nonvolatile memory cells may include respective nonvolatile resistive devices electrically coupled in series with corresponding cell transistors. A controller is also provided, which may be coupled to the memory device. The controller can be configured to drive the memory device with signals that support dual programming of: (i) the nonvolatile resistive devices; and (ii) interface states within the cell transistors, during operations to write data into the memory device.