This study brings together Bayesian networks, topic models, hierarchical Bayes modeling and nonparametric Bayesian methods to build a framework for efficiently designing and implementing a family of (non)parametric Bayesian mixture models. Bayesian mixture models, including Bayesian topic models, have shown themselves to be a useful tool for modeling and discovering latent structure in a number of domains. We introduce a modeling framework, networks of mixture blocks, that brings together these developments in a way that facilitates the definition and implementation of complex (non)parametric Bayesian networks for data with partitioned structure. Networks of mixture blocks can be viewed as Bayesian networks that have been factored into a network of sub-models, mixture blocks, which are conditionally independent of each other given the introduction of auxiliary partition variables. We use this framework to develop several novel nonparametric Bayesian models for collaborative filtering and text modeling.