Disclosed are battery management systems with control logic for battery state estimation (BSE), methods for making/using/assembling a battery cell with a reference electrode, and electric drive vehicles equipped with a traction battery pack and BSE capabilities. In an example, a battery cell assembly includes a battery housing with an electrolyte composition stored within the battery housing. The electrolyte composition transports ions between working electrodes. A first working (anode) electrode is attached to the battery housing in electrochemical contact with the electrolyte composition. Likewise, a second working (cathode) electrode is attached to the battery housing in electrochemical contact with the electrolyte composition. A reference electrode is interposed between the first and second working electrodes, placed in electrochemical contact with the electrolyte composition. The reference electrode and one or both working electrodes cooperate to output a half-cell voltage signal that is indicative of a battery state of the battery cell assembly.