This study introduces the S1S2-Water dataset – a global reference dataset for training, validation and testing of convolutional neural networks for semantic segmentation of surface water bodies in publicly available Sentinel-1 and Sentinel-2 satellite images. The dataset consists of 65 triplets of Sentinel-1 and Sentinel-2 images with quality checked binary water mask. Samples are drawn globally on the basis of the Sentinel-2 tile-grid (100 x 100 km) under consideration of predominant landcover and availability of water bodies. Each sample is complemented with metadata and Digital Elevation Model (DEM) raster from the Copernicus DEM. On the basis of this dataset we carry out performance evaluation of convolutional neural network architectures to segment surface water bodies from Sentinel-1 and Sentinel-2 images. We specifically evaluate the influence of image bands, elevation features and data augmentation on the segmentation performance and identify best-performing baseline-models. The model for Sentinel-1 achieves an Intersection Over Union of 0.85, Precision of 0.93 and Recall of 0.90 on the test data. For Sentinel-2 the best model produces an Intersection Over Union of 0.96, Precision of 0.99 and Recall of 0.97 respectively. We also evaluate the performance impact when a model is trained on permanent water data and applied to independent test scenes of floods.