Label scarcity is a bottleneck for improving task performance in specialised domains. We propose a novel compositional transfer learning framework (DOT5 1 ) for zeroshot 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 indomain 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 summarisation and embedding learning. DOT5 demonstrates the effectiveness of compositional transfer learning through multi-task learning. In particular, DOT5 outperforms the current stateof-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. * Work done at Microsoft Health Futures. 1 DOT5 (read as "dot five"): Domain Compositional ZerOshot T5.