We propose the first joint-task learning framework for brain and vessel segmentation (JoB-VS) from Time-of-Flight Magnetic Resonance images. Unlike state-of-the-art vessel segmentation methods, our approach avoids the pre-processing step of implementing a model to extract the brain from the volumetric input data. Skipping this additional step makes our method an end-to-end vessel segmentation framework. JoB-VS uses a lattice architecture that favors the segmentation of structures of different scales (e.g., the brain and vessels). Its segmentation head allows the simultaneous prediction of the brain and vessel mask. Moreover, we generate data augmentation with adversarial examples, which our results demonstrate to enhance the performance. JoB-VS achieves 70.03% mean AP and 69.09% F1-score in the OASIS-3 dataset and is capable of generalizing the segmentation in the IXI dataset. These results show the adequacy of JoB-VS for the challenging task of vessel segmentation in complete TOF-MRA images.