Abstract: In medicine, comorbidities refer to the presence of multiple, co-occurring diseases. Due to their co-occurring nature, the course of one comorbidity is often highly dependent on the course of the other disease and, hence, treatments can have significant spill-over effects. Despite the prevalence of comorbidities among patients, a comprehensive statistical framework for modeling the longitudinal dynamics of comorbidities is missing. In this paper, we propose a probabilistic model for analyzing comorbidity dynamics over time in patients. Specifically, we develop a coupled hidden Markov model with a personalized, non-homogeneous transition mechanism, named Comorbidity-HMM. The specification of our Comorbidity-HMM is informed by clinical research: (1) It accounts for different disease states (i. e., acute, stable) in the disease progression by introducing latent states that are of clinical meaning. (2) It models a coupling among the trajectories from comorbidities to capture co-evolution dynamics. (3) It considers between-patient heterogeneity (e. g., risk factors, treatments) in the transition mechanism. Based on our model, we define a spill-over effect that measures the indirect effect of treatments on patient trajectories through coupling (i. e., through comorbidity co-evolution). We evaluated our proposed Comorbidity-HMM based on 675 health trajectories where we investigate the joint progression of diabetes mellitus and chronic liver disease. Compared to alternative models without coupling, we find that our Comorbidity-HMM achieves a superior fit. Further, we quantify the spill-over effect, that is, to what extent diabetes treatments are associated with a change in the chronic liver disease from an acute to a stable disease state. To this end, our model is of direct relevance for both treatment planning and clinical research in the context of comorbidities.