Regions around the world experience adverse climate-change-induced conditions that pose severe risks to the normal and sustainable operations of modern societies. Extreme weather events, such as floods, rising sea levels, and storms, stand as characteristic examples that impair the core services of the global ecosystem. Especially floods have a severe impact on human activities, hence, early and accurate delineation of the disaster is of top priority since it provides environmental, economic, and societal benefits and eases relief efforts. In this article, we introduce OmbriaNet, a deep neural network architecture, based on convolutional neural networks, that detects changes between permanent and flooded water areas by exploiting the temporal differences among flood events extracted by different sensors. To demonstrate the potential of the proposed approach, we generated OMBRIA, a bitemporal and multimodal satellite imagery dataset for image segmentation through supervised binary classification. It consists of a total number of 3.376 images, synthetic aperture radar imagery from Sentinel-1, and multispectral imagery from Sentinel-2, accompanied with ground-truth binary images produced from data derived by experts and provided from the Emergency Management Service of the European Space Agency Copernicus Program. The dataset covers 23 flood events around the globe, from 2017 to 2021. We collected, co-registrated and preprocessed the data in Google Earth Engine. To validate the performance of our method, we performed different benchmarking experiments on the OMBRIA dataset and we compared with several competitive state-of-the-art techniques. The experimental analysis demonstrated that the proposed formulation is able to produce high-quality flood maps, achieving a superior performance over the state-of-the-art. We provide OMBRIA dataset, as well as OmbriaNet code at: https://github.com/geodrak/OMBRIA .