A new advanced mathematical model is proposed to accurately simulate the behavior of all-solid-state Li-ion batteries. The model includes charge-transfer kinetics at both electrode/electrolyte interfaces, diffusion and migration of mobile lithium ions in the electrolyte and positive electrode. In addition, electrical double layers are considered, representing the space-charge separation phenomena at both electrode/electrolyte interfaces. The model can be used to simultaneously study the individual overpotential and impedance contributions together with concentration gradients and electric fields across the entire battery stack. Both galvanostatic discharge and impedance simulations have been experimentally validated with respect to 0.7 mAh Li/LiPON/LiCoO2 thin film, all-solid-state, batteries. The model shows good agreement with galvanostatic discharging, voltage relaxation upon current interruption, and impedance measurements. From the performed AC and DC simulations it can be concluded that the overpotential across the LiPON electrolyte is most dominant and is therefore an important rate-limiting factor. In addition, it is found that both ionic and electronic diffusion coefficients in the LiCoO2 electrode seriously influence the battery performance. The present model is generally applicable to all-solid-state batteries where combined ionic and electronic transport takes place and allows for optimizing the battery components to increase the effective energy density, which leads to a decreasing demand for materials and costs.