Vascular network analysis is crucial to define the tumoral architecture and then diagnose the cancer subtype. However, automatic vascular network segmentation from Hematoxylin and Eosin (H&E) staining histopathological images is still a challenge due to the background complexity. Moreover, there is a lack of large manually annotated vascular network databases. In this paper, we propose a method that reduces reliance on labeled data through semi-supervised learning (SSL). Additionally, considering the correlation between tumor classification and vascular segmentation, we propose a multi-task learning (MTL) model that can simultaneously segment the vascular network using SSL and predict the tumor class in a supervised context. This multi-task learning procedure offers an end-to-end machine learning solution to joint vascular network segmentation and tumor classification. Experiments were carried out on a database of histopathological images of renal cell carcinoma (RCC) and then tested on both own RCC and open-source TCGA datasets. The results show that the proposed MTL-SSL model outperforms the conventional supervised-learning segmentation approach.