Documents often have inherently parallel structure: they may consist of a text and ries, or an abstract and a body, or parts presenting alternative views on the same problem. Revealing relations between the parts by jointly segmenting and predicting links between the segments, would help to visualize such documents and construct friendlier user interfaces. To address this problem, we propose an unsupervised Bayesian model for joint discourse segmentation and alignment. We apply our method to the "English as a second language" podcast dataset where each episode is composed of two parallel parts: a story and an explanatory lecture. The predicted topical links uncover hidden relations between the stories and the lectures. In this domain, our method achieves competitive results, rivaling those of a previously proposed supervised technique.