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Recently, several Bayesian deep learning methods have been proposed for semi-supervised medical image segmentation. Although they have achieved promising results on medical benchmarks, some problems are still existing. Firstly, their overall architectures belong to the discriminative models, and hence, in the early stage of training, they only use labeled data for training, which might make them overfit to the labeled data. Secondly, in fact, they are only partially based on Bayesian deep learning, as their overall architectures are not designed under the Bayesian framework. However, unifying the overall architecture under the Bayesian perspective can make the architecture have a rigorous theoretical basis, so that each part of the architecture can have a clear probabilistic interpretation. Therefore, to solve the problems, we propose a new generative Bayesian deep learning (GBDL) architecture. GBDL belongs to the generative models, whose target is to estimate the joint distribution of input medical volumes and their corresponding labels. Estimating the joint distribution implicitly involves the distribution of data, so both labeled and unlabeled data can be utilized in the early stage of training, which alleviates the potential overfitting problem. Besides, GBDL is completely designed under the Bayesian framework, and thus we give its full Bayesian formulation, which lays a theoretical probabilistic foundation for our architecture. Extensive experiments show that our GBDL outperforms previous state-of-the-art methods in terms of four commonly used evaluation indicators on three public medical datasets.