As all-solid-state batteries (SSBs) develop as an alternative to traditional cells, a thorough theoretical understanding of driving forces behind battery operation is needed. We present a fully first-principles-informed model of potential profiles in SSBs and apply the model to the Li/LiPON/Li_{x}CoO_{2} system. The model predicts interfacial potential drops driven by both electron transfer and Li^{+} space-charge layers that vary with the SSB's state of charge. The results suggest a lower electronic ionization potential in the solid electrolyte favors Li^{+} transport, leading to higher discharge power.