We propose a Bayesian undirected graphical model for semi-supervised multi-view learning (BMVL). This model makes explicit the previously unstated assumptions of a large class of semi-supervised multi-view learning algorithms, and clarifies the circumstances under which these assumptions fail. Building upon new insights from this model, we propose an improved method for BMVL: in particular, we derive a novel co-training kernel for Gaussian Process classifiers. Unlike some previous methods for multi-view learning, the resulting approach is convex and avoids local-maxima problems. Further, it automatically estimates how much each view should be trusted, and thus accommodates noisy or unreliable views. Experiments show that the approach is more accurate than previous multi-view learning algorithms.