Protein-protein interactions are central mediators in many biological processes. Accurately predicting the effects of mutations on interactions is crucial for guiding the modulation of these interactions, thereby playing a significant role in therapeutic development and drug discovery. Mutations generally affect interactions hierarchically across three levels: mutated residues exhibit different sidechain conformations, which lead to changes in the backbone conformation, eventually affecting the binding affinity between proteins. However, existing methods typically focus only on sidechain-level interaction modeling, resulting in suboptimal predictions. In this work, we propose a self-supervised multi-level pre-training framework, ProMIM, to fully capture all three levels of interactions with well-designed pretraining objectives. Experiments show ProMIM outperforms all the baselines on the standard benchmark, especially on mutations where significant changes in backbone conformations may occur. In addition, leading results from zero-shot evaluations for SARS-CoV-2 mutational effect prediction and antibody optimization underscore the potential of ProMIM as a powerful next-generation tool for developing novel therapeutic approaches and new drugs.