Emotion Recognition in Conversation (ERC) has gained much attention from the NLP community recently. Some models concentrate on leveraging commonsense knowledge or multi-task learning to help complicated emotional reasoning. However, these models neglect direct utterance-knowledge interaction. In addition, these models utilize emotion-indirect auxiliary tasks, which provide limited affective information for the ERC task. To address the above issues, we propose a Knowledge-Interactive Network with sentiment polarity intensity-aware multi-task learning, namely KI-Net, which leverages both commonsense knowledge and sentiment lexicon to augment semantic information. Specifically, we use a self-matching module for internal utterance-knowledge interaction. Considering correlations with the ERC task, a phrase-level Sentiment Polarity Intensity Prediction (SPIP) task is devised as an auxiliary task. Experiments show that all knowledge integration, self-matching and SPIP modules improve the model performance respectively on three datasets. Moreover, our KI-Net model shows 1.04% performance improvement over the state-of-the-art model on the IEMOCAP dataset.