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Multi-task learning promises better model generalization on a target task by jointly optimizing it with an auxiliary task. However, the current practice requires additional labeling efforts for the auxiliary task, while not guaranteeing better model performance. In this paper, we find that jointly training a dense prediction (target) task with a self-supervised (auxiliary) task can consistently improve the performance of the target task, while eliminating the need for labeling auxiliary tasks. We refer to this joint training as Composite Learning (CompL). Experiments of CompL on monocular depth estimation, semantic segmentation, and boundary detection show consistent performance improvements in fully and partially labeled datasets. Further analysis on depth estimation reveals that joint training with self-supervision outperforms most labeled auxiliary tasks. We also find that CompL can improve model robustness when the models are evaluated in new domains. These results demonstrate the benefits of self-supervision as an auxiliary task, and establish the design of novel task-specific self-supervised methods as a new axis of investigation for future multi-task learning research.