Label scarcity is a bottleneck for improving task performance in specialized domains. We propose a novel compositional transfer learning framework (DoT51) for zero-shot domain transfer. Without access to in-domain labels, DoT5 jointly learns domain knowledge (from masked language modelling of unlabelled in-domain free text) and task knowledge (from task training on more readily available general-domain data) in a multi-task manner. To improve the transferability of task training, we design a strategy named NLGU: We simultaneously train natural language generation (NLG) for in-domain label-to-data generation, which enables data augmentation for self-finetuning and natural language understanding (NLU) for label prediction. We evaluate DoT5 on the biomedical domain and the resource-lean subdomain of radiology, focusing on natural language inference, text summarization, and embedding learning. DoT5 demonstrates the effectiveness of compositional transfer learning through multi-task learning. In particular, DoT5 outperforms the current state-of-the-art in zero-shot transfer by over 7 absolute points in accuracy on RadNLI. We validate DoT5 with ablations and a case study demonstrating its ability to solve challenging NLI examples requiring in-domain expertise.