We present an unsupervised model for joint phrase alignment and extraction using nonparametric Bayesian methods and inversion transduction grammars (ITGs). The key contribution is that phrases of many granularities are included directly in the model through the use of a novel formulation that memorizes phrases generated not only by terminal, but also non-terminal symbols. This allows for a completely probabilistic model that is able to create a phrase table that achieves competitive accuracy on phrase-based machine translation tasks directly from unaligned sentence pairs. Experiments on several language pairs demonstrate that the proposed model matches the accuracy of traditional two-step word alignment/phrase extraction approach while reducing the phrase table to a fraction of the original size.