Here, the use of an hybrid methodology, VarDyn, combining minimal physically-based constraints with a variational scheme, is demonstrated to improve mapping capabilities of sea surface height (SSH) and temperature (SST). Synthesizing multi-modal satellite observations, VarDyn improves the accuracy of SSH and SST maps compared to operational products, both in terms of RMSE and effective spatial resolution. Expected, most improvements occur in high energetic ocean regions. Still, the accuracy of SSH maps also slightly improves in low energetic regions, which is a clear improvement compared to other methods. VarDyn SSH fields and associated geostrophic velocities further reveal strong agreements with newly available high-resolution instantaneous SWOT estimates. Remarkably, the assimilation of SST especially benefits SSH reconstruction when only 2 altimeters are available. The VarDyn method thus opens robust means to refine climate SSH records, jointly assimilating SSH from 2 altimeters and SST from microwave sensors.