We propose a novel approach for rapid segmentation of flooded buildings by fusing multiresolution, multisensor, and multitemporal satellite imagery in a convolutional neural network. Our model significantly expedites the generation of satellite imagery-based flood maps, crucial for first responders and local authorities in the early stages of flood events. By incorporating multitemporal satellite imagery, our model allows for rapid and accurate post-disaster damage assessment and can be used by governments to better coordinate medium- and long-term financial assistance programs for affected areas. The network consists of multiple streams of encoder-decoder architectures that extract spatiotemporal information from medium-resolution images and spatial information from high-resolution images before fusing the resulting representations into a single medium-resolution segmentation map of flooded buildings. We compare our model to state-of-the-art methods for building footprint segmentation as well as to alternative fusion approaches for the segmentation of flooded buildings and find that our model performs best on both tasks. We also demonstrate that our model produces highly accurate segmentation maps of flooded buildings using only publicly available medium-resolution data instead of significantly more detailed but sparsely available very high-resolution data. We release the first open-source dataset of fully preprocessed and labeled multiresolution, multispectral, and multitemporal satellite images of disaster sites along with our source code.