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The study of the retinal vasculature is a fundamental stage in the screening and diagnosis of many diseases. A complete retinal vascular analysis requires to segment and classify the blood vessels of the retina into arteries and veins (A/V). Early automatic methods approached these segmentation and classification tasks in two sequential stages. However, currently, these tasks are approached as a joint semantic segmentation task, as the classification results highly depend on the effectiveness of the vessel segmentation. In that regard, we propose a novel approach for the simultaneous segmentation and classification of the retinal A/V from eye fundus images. In particular, we propose a novel method that, unlike previous approaches, and thanks to a novel loss, decomposes the joint task into three segmentation problems targeting arteries, veins and the whole vascular tree. This configuration allows to handle vessel crossings intuitively and directly provides accurate segmentation masks of the different target vascular trees. The provided ablation study on the public Retinal Images vessel Tree Extraction (RITE) dataset demonstrates that the proposed method provides a satisfactory performance, particularly in the segmentation of the different structures. Furthermore, the comparison with the state of the art shows that our method achieves highly competitive results in A/V classification, while significantly improving vascular segmentation. The proposed multi-segmentation method allows to detect more vessels and better segment the different structures, while achieving a competitive classification performance. Also, in these terms, our approach outperforms the approaches of various reference works. Moreover, in contrast with previous approaches, the proposed method allows to directly detect the vessel crossings, as well as preserving the continuity of A/V at these complex locations.