This paper presents a multi-task learning approach to natural language inference (NLI) and question entailment (RQE) in the biomedical domain. Recognizing textual inference relations and question similarity can address the issue of answering new consumer health questions by mapping them to Frequently Asked Questions on reputed websites like the NIH. We show that leveraging information from parallel tasks across domains along with medical knowledge integration allows our model to learn better biomedical feature representations. Our final models for the NLI and RQE tasks achieve the 4th and 2nd rank on the shared-task leaderboard respectively.