Determining interactions between entities and the overall organization and clustering of nodes in networks is a major challenge when analyzing biological and social network data. Here we extend the Indian Buffet Process (IBP), a nonparametric Bayesian model, to integrate noisy interaction scores with properties of individual entities for inferring interaction networks and clustering nodes within these networks. We present an application of this method to study how microRNAs regulate mRNAs in cells. Analysis of synthetic and real data indicates that the method improves upon prior methods, correctly recovers interactions and clusters, and provides accurate biological predictions.