Aiming at the development of a monolithic integrated all-solid-state self-rechargeable power unit, we perform a V-I characteristics compatibility study for the integration of such a device having a thin-film silicon multi-junction photovoltaic (PV) module and a thin-film solid Li//lithium phosphorus oxynitride//LiCoO2 battery. The battery and PV module are connected to mimic a monolithic module-to-storage cell device and the performance of this device in various temperature conditions has been tested. Few issues regarding the matching of the battery and PV module characteristics are identified for improvement. The concept of the integrated all-solid-state PV-battery solution appears viable especially in three-terminal device configuration.