Geophysical monitoring of geologic carbon sequestration is critical for risk assessment during and after carbon dioxide (CO2) injection. Integration of multiple geophysical measurements is a promising approach to achieve high-resolution reservoir monitoring. However, joint inversion of large geophysical data is challenging due to high computational costs and difficulties in effectively incorporating measurements from different sources and with different resolutions. This study develops a differentiable physics model for large-scale joint inverse problems with reparameterization of model variables by deep neural networks and implementation of a differentiable programming approach of the forward model. The main novelty is the use of automatic differentiation and parallel computing for efficient multiphysics data assimilation. The application to the Sleipner benchmark model demonstrates that the proposed method is effective in estimation of reservoir properties from seismic and resistivity data and shows promising results for CO2 storage monitoring.