Mapping water extent during a flood event is essential for effective disaster management throughout all phases: mitigation, preparedness, response, and recovery. In particular, during the response stage, when timely and accurate information is important, Synthetic Aperture Radar (SAR) data are primarily employed to produce water extent maps. Recently, leveraging the complementary characteristics of SAR and MSI data through a multimodal approach has emerged as a promising strategy for advancing water extent mapping using deep learning models. This approach is particularly beneficial when timely post-flood observations, acquired during or shortly after the flood peak, are limited, as it enables the use of all available imagery for more accurate post-flood water extent mapping. However, the adaptive integration of partially available MSI data into the SAR-based post-flood water extent mapping process remains underexplored. To bridge this research gap, we propose the Spatially Masked Adaptive Gated Network (SMAGNet), a multimodal deep learning model that utilizes SAR data as the primary input for post-flood water extent mapping and integrates complementary MSI data through feature fusion. In experiments on the C2S-MS Floods dataset, SMAGNet consistently outperformed other multimodal deep learning models in prediction performance across varying levels of MSI data availability. Furthermore, we found that even when MSI data were completely missing, the performance of SMAGNet remained statistically comparable to that of a U-Net model trained solely on SAR data. These findings indicate that SMAGNet enhances the model robustness to missing data as well as the applicability of multimodal deep learning in real-world flood management scenarios.