Knowledge distillation (KD) addresses model compression by distilling knowledge from a large model (teacher) to a smaller one (student). The existing distillation approaches mainly focus on using different criteria to align the sample representations learned by the student and the teacher, while they fail to transfer the class representations. Good class representations can benefit the sample representation learning by shaping the sample representation distribution. On the other hand, the existing approaches enforce the student to fully imitate the teacher while ignoring the fact that the teacher is typically not perfect. Although the teacher has learned rich and powerful representations, it also contains unignorable bias knowledge which is usually induced by the context prior (e.g., background) in the training data. To address these two issues, in this paper, we propose comprehensive, interventional distillation (CID) that captures both sample and class representations from the teacher while removing the bias with causal intervention. Different from the existing literature that uses the softened logits of the teacher as the training targets, CID considers the softened logits as the context information of an image, which is further used to remove the biased knowledge based on causal inference. Keeping the good representations while removing the bad bias enables CID to have a better generalization ability on test data and a better transferability across different datasets against the existing state-of-the-art approaches, which is demonstrated by extensive experiments on several benchmark datasets.