Significance Genetic recombination processes, such as reassortment, make it complex or impossible to use standard phylogenetic and phylodynamic methods. This is due to the fact that the shared evolutionary history of individuals has to be represented by a phylogenetic network instead of a tree. We therefore require novel approaches that allow us to coherently model these processes and that allow us to perform inference in the presence of such processes. Here, we introduce an approach to infer reassortment networks of segmented viruses using a Markov chain Monte Carlo approach. Our approach allows us to study different aspects of the reassortment process and allows us to show fitness benefits of reassortment events in seasonal human influenza viruses.