Comorbidities, defined as the presence of co-existing diseases, progress through complex temporal patterns among patients. Learning such dynamics from electronic health records is crucial for understanding the coevolution of diseases. In general, medical records are represented through temporal sequences of clinical variables together with their diagnosis. However, we consider the specific problem where most of the diagnoses are missing. We present a novel probabilistic generative model with a three-fold objective: (i) identify and segment the medical history of patients into treatments associated with comorbidities; (ii) learn the model associated with each identified disease treatment; and (iii) discover subtypes of patients with similar coevolution of comorbidities.To this end, the model considers a latent structure for the sequences, where patients are modeled by a latent class defined by the evolution of their comorbidities, and each observed medical event of their clinical history is associated with a latent disease. The learning process is performed using an Expectation-Maximization algorithm that considers the exponential number of configurations of the latent variables and is efficiently solved with dynamic programming.The evaluation of the method is carried out both on synthetic and real world data: the experiments on synthetic data show that the learning procedure allows the generative model underlying the data to be recovered; the experiments on real medical data show accurate results in the segmentation of sequences into different treatments, subtyping of patients and diagnosis imputation.We present an interpretable generative model that handles the incompleteness of EHRs and describes the different joint evolution of coexisting diseases depending on the active comorbidities of the patient at each moment.