In order to better understand the rationale behind model behavior, recent works have exploited providing interpretation to support the inference prediction. However, existing methods tend to provide human-unfriendly interpretation, and are prone to sub-optimal performance due to one-side promotion, i.e. either inference promotion with interpretation or vice versa. In this paper, we propose a multi-level Mutual Promotion mechanism for self-evolved Inference and sentence-level Interpretation (MPII). Specifically, from the model-level, we propose a Step-wise Integration Mechanism to jointly perform and deeply integrate inference and interpretation in an autoregressive manner. From the optimization-level, we propose an Adversarial Fidelity Regularization to improve the fidelity between inference and interpretation with the Adversarial Mutual Information training strategy. Extensive experiments on NLI and CQA tasks reveal that the proposed MPII approach can significantly outperform baseline models for both the inference performance and the interpretation quality.