In spite of great advancements of machine reading comprehension (RC), existing RC models are still vulnerable and not robust to different types of adversarial examples. Neural models over-confidently predict wrong answers to semantic different adversarial examples, while over-sensitively predict wrong answers to semantic equivalent adversarial examples. Existing methods which improve the robustness of such neural models merely mitigate one of the two issues but ignore the other. In this paper, we address the over-confidence issue and the over-sensitivity issue existing in current RC models simultaneously with the help of external linguistic knowledge. We first incorporate external knowledge to impose different linguistic constraints (entity constraint, lexical constraint, and predicate constraint), and then regularize RC models through posterior regularization. Linguistic constraints induce more reasonable predictions for both semantic different and semantic equivalent adversarial examples, and posterior regularization provides an effective mechanism to incorporate these constraints. Our method can be applied to any existing neural RC models including state-of-the-art BERT models. Extensive experiments show that our method remarkably improves the robustness of base RC models, and is better to cope with these two issues simultaneously.