Intimate ecological interactions, such as those between parasites and their hosts, may persist over long time spans, coupling the evolutionary histories of the lineages involved. Most methods that reconstruct the coevolutionary history of such interactions make the simplifying assumption that parasites have a single host. Many methods also focus on congruence between host and parasite phylogenies, using cospeciation as the null model. However, there is an increasing body of evidence suggesting that the host ranges of parasites are more complex: that host ranges often include more than one host and evolve via gains and losses of hosts rather than through cospeciation alone. Here, we develop a Bayesian approach for inferring coevolutionary history based on a model accommodating these complexities. Specifically, a parasite is assumed to have a host repertoire, which includes both potential hosts and one or more actual hosts. Over time, potential hosts can be added or lost, and potential hosts can develop into actual hosts or vice versa. Thus, host colonization is modeled as a two-step process that may potentially be influenced by host relatedness. We first explore the statistical behavior of our model by simulating evolution of host-parasite interactions under a range of parameter values. We then use our approach, implemented in the program RevBayes, to infer the coevolutionary history between 34 Nymphalini butterfly species and 25 angiosperm families. Our analysis suggests that host relatedness among angiosperm families influences how easily Nymphalini lineages gain new hosts.