Data augmentation is a simple yet effective way to improve the robustness of deep neural networks (DNNs). Diversity and hardness are two complementary dimensions of data augmentation to achieve robustness. For example, AugMix explores random compositions of a diverse set of augmentations to enhance broader coverage, while adversarial training generates adversarially hard samples to spot the weakness. Motivated by this, we propose a data augmentation framework, termed AugMax, to unify the two aspects of diversity and hardness. AugMax first randomly samples multiple augmentation operators and then learns an adversarial mixture of the selected operators. Being a stronger form of data augmentation, AugMax leads to a significantly augmented input distribution which makes model training more challenging. To solve this problem, we further design a disentangled normalization module, termed DuBIN (Dual-Batch-and-Instance Normalization), that disentangles the instance-wise feature heterogeneity arising from AugMax. Experiments show that AugMax-DuBIN leads to significantly improved out-of-distribution robustness, outperforming prior arts by 3.03%, 3.49%, 1.82% and 0.71% on CIFAR10-C, CIFAR100-C, Tiny ImageNet-C and ImageNet-C. Codes and pretrained models are available: https://github.com/VITA-Group/AugMax.