We propose an approach for estimating the relative pose between calibrated image pairs by jointly exploiting points, lines, and their coincidences in a hybrid manner. We investigate all possible configurations where these data modalities can be used together and review the minimal solvers available in the literature. Our hybrid framework combines the advantages of all configurations, enabling robust and accurate estimation in challenging environments. In addition, we design a method for jointly estimating multiple vanishing point correspondences in two images, and a bundle adjustment that considers all relevant data modalities. Experiments on various indoor and outdoor datasets show that our approach outperforms point-based methods, improving AUC@10$^\circ$ by 1-7 points while running at comparable speeds. The source code of the solvers and hybrid framework will be made public.