We combine a three-phase, three-dimensional reconstruction of a LiCoO2 battery cathode based on focused ion-beam/scanning electron microscopy (FIB/SEM) imaging with an electrochemical model. The model considers the electric potential and lithium/salt concentration distribution in both the liquid electrolyte and the solid active-material phases. In contrast to previously presented models, we spatially resolve the carbon-binder phase to provide a more realistic description of the electric potential. We observe that carbon-binder coverage of the solid electrolyte interface (SEI) impedes local surface reactions and thus affects lithium redistribution. For the considered cathode, the total surface to volume ratio of the SEI is reduced from 11.2×105 to 6.5×105 m2 m−3 when the carbon-binder phase is modelled explicitly. This leads to increased inhomogeneity of the lithium concentration in active-material grains during charging. Additionally, we study lithium/salt concentration in the electrolyte, revealing gradients between 0.9 and 1.5kmolm−3 depending on the distance to the separator. This is significant because the lithium/salt concentration directly affects the ion transport properties of the electrolyte.