Empathy is an important characteristic to be considered when building a more intelligent and humanized dialogue agent. However, existing methods did not fully comprehend empathy as a complex process involving three aspects: cognition, affection and behavior. In this paper, we propose CAB, a novel framework that takes a comprehensive perspective of cognition, affection and behavior to generate empathetic responses. For cognition, we build paths between critical keywords in the dialogue by leveraging external knowledge. This is because keywords in a dialogue are the core of sentences. Building the logic relationship between keywords, which is overlooked by the majority of existing works, can improve the understanding of keywords and contextual logic, thus enhance the cognitive ability. For affection, we capture the emotional dependencies with dual latent variables that contain both interlocutors' emotions. The reason is that considering both interlocutors' emotions simultaneously helps to learn the emotional dependencies. For behavior, we use appropriate dialogue acts to guide the dialogue generation to enhance the empathy expression. Extensive experiments demonstrate that our multi-perspective model outperforms the state-of-the-art models in both automatic and manual evaluation.