Accurate and high-resolution hydrological models are crucially needed, especially for important socioeconomic issues related to floods and droughts, but are faced with data and model uncertainties which can be reduced by maximizing information integration from multisource data. This work focuses on improving the integration of satellite and in situ land surface data into spatially distributed hydrological models. The Hybrid Data Assimilation and Parameter Regionalization (HDA-PR) approach incorporating learnable regionalization mappings, based on neural networks into the differentiable spatially distributed hydrological model SMASH, is modified to account for satellite-based moisture maps in addition to discharge at gauging stations and basin physical descriptors maps. Regional optimizations of a spatially distributed conceptual model are performed on a flash-flood-prone area located in the South of France, and their accuracy and robustness are evaluated in terms of simulated discharge and moisture against observations. In general, the integration of satellite-derived soil moisture data alongside traditional observed streamflow measurements during calibration procedures has demonstrated notable improvements in hydrological performance, both in terms of simulated discharge and moisture. This is achieved thanks to an improved learning of regionalization of model conceptual parameters with HDA-PR integrating satellite-based moisture through the RMSE metric adapted to a spatially distributed model with variational data assimilation. This study provides a solid foundation for advanced data assimilation of multi-source data into learnable spatially distributed differentiable geophysical models.