Data sets of interactions, such as human and animal social networks, exhibit informative patterns in their structure. Communities appear as individuals cluster into tightly knit social groups, often along the lines of shared attributes. Hierarchies emerge as interactions tend to orient in a consistent direction, for example as people name higher status peers more often as their friends. Probabilistic models are used to leverage these tendencies to infer these underlying structures from the network alone. In this work we define a Bayesian model that jointly models these processes and further explores the possible interplay between them. This framework allows us to quantify the degree of both community structure and hierarchy present in a system and further to quantify the strength of interaction between the two. To what extent does community membership influence social status? And vice versa? By fitting the resulting model we obtain rich descriptions of a variety of data sets and consistently find strong evidence of interactions between community structure and hierarchy.