Building footprints and road networks are important inputs for a great deal of services. For instance, building maps are useful for urban planning, whereas road maps are essential for disaster response services. Traditionally, building and road maps are manually generated by remote sensing experts or land surveying, occasionally assisted by semi-automatic tools. In the last decade, deep learning-based approaches have demonstrated their capabilities to extract these elements automatically and accurately from remote sensing imagery. The building footprint and road network detection problem can be considered a multi-class semantic segmentation task, that is, a single model performs a pixel-wise classification on multiple classes, optimizing the overall performance. However, depending on the spatial resolution of the imagery used, both classes may coexist within the same pixel, drastically reducing their separability. In this regard, binary decomposition techniques, which have been widely studied in the machine learning literature, are proved useful for addressing multi-class problems. Accordingly, the multi-class problem can be split into multiple binary semantic segmentation sub-problems, specializing different models for each class. Nevertheless, in these cases, an aggregation step is required to obtain the final output labels. Additionally, other novel approaches, such as multi-task learning, may come in handy to further increase the performance of the binary semantic segmentation models. Since there is no certainty as to which strategy should be carried out to accurately tackle a multi-class remote sensing semantic segmentation problem, this paper performs an in-depth study to shed light on the issue. For this purpose, open-access Sentinel-1 and Sentinel-2 imagery (at 10 m) are considered for extracting buildings and roads, making use of the well-known U-Net convolutional neural network. It is worth stressing that building and road classes may coexist within the same pixel when working at such a low spatial resolution, setting a challenging problem scheme. Accordingly, a robust experimental study is developed to assess the benefits of the decomposition strategies and their combination with a multi-task learning scheme. The obtained results demonstrate that decomposing the considered multi-class remote sensing semantic segmentation problem into multiple binary ones using a One-vs.-All binary decomposition technique leads to better results than the standard direct multi-class approach. Additionally, the benefits of using a multi-task learning scheme for pushing the performance of binary segmentation models are also shown.