Protein functions are characterized by interactions with proteins, drugs, and other biomolecules. Understanding these interactions is essential for deciphering the molecular mechanisms underlying biological processes and developing new therapeutic strategies. Current computational methods mostly predict interactions based on either molecular network or structural information, without integrating them within a unified multi-scale framework. While a few multi-view learning methods are devoted to fusing the multi-scale information, these methods tend to rely intensively on a single scale and under-fitting the others, likely attributed to the imbalanced nature and inherent greediness of multi-scale learning. To alleviate the optimization imbalance, we present MUSE, a multi-scale representation learning framework based on a variant expectation maximization to optimize different scales in an alternating procedure over multiple iterations. This strategy efficiently fuses multi-scale information between atomic structure and molecular network scale through mutual supervision and iterative optimization. MUSE outperforms the current state-of-the-art models not only in molecular interaction (protein-protein, drug-protein, and drug-drug) tasks but also in protein interface prediction at the atomic structure scale. More importantly, the multi-scale learning framework shows potential for extension to other scales of computational drug discovery.