This paper describes an unsupervised dynamic graphical model for morphological segmentation and bilingual morpheme alignment for statistical machine translation. The model extends Hidden Semi-Markov chain models by using factored output nodes and special structures for its conditional probability distributions. It relies on morpho-syntactic and lexical source-side information (part-of-speech, morphological segmentation) while learning a morpheme segmentation over the target language. Our model outperforms a competitive word alignment system in alignment quality. Used in a monolingual morphological segmentation setting it substantially improves accuracy over previous state-of-the-art models on three Arabic and Hebrew datasets.