There is a growing interest in the development of automated data processing workflows that provide reliable, high spatial resolution land cover maps. However, high-resolution remote sensing images are not always affordable. Taking into account the free availability of Sentinel-2 satellite data, in this work we propose a deep learning model to generate high-resolution segmentation maps from low-resolution inputs in a multi-task approach. Our proposal is a dual-network model with two branches: the Single Image Super-Resolution branch, that reconstructs a high-resolution version of the input image, and the Semantic Segmentation Super-Resolution branch, that predicts a high-resolution segmentation map with a scaling factor of 2. We performed several experiments to find the best architecture, training and testing on a subset of the S2GLC 2017 dataset. We based our model on the DeepLabV3+ architecture, enhancing the model and achieving an improvement of 5% on IoU and almost 10% on the recall score. Furthermore, our qualitative results demonstrate the effectiveness and usefulness of the proposed approach.