We outline a bidirectional translation system that converts sentences from American Sign Language (ASL) to English, and vice versa. To perform machine translation between ASL and English, we utilize a generative approach. Specifically, we employ an adjustment to the IBM word-alignment model 1 (IBM WAM1), where we define language models for English and ASL, as well as a translation model, and attempt to generate a translation that maximizes the posterior distribution defined by these models. Then, using these models, we are able to quantify the concepts of fluency and faithfulness of a translation between languages.