Binge eating disorder (BED) is the most prevalent eating disorder. However, current diagnostic frameworks remain largely grounded in symptom-based criteria rather than underlying biological mechanisms, thereby limiting early detection and the development of biologically-informed interventions. Emerging studies have begun to investigate the neurobiological signatures of BED, yet their findings are often difficult to generalize due to the reliance on hypothesis-driven parametric models, single-modality analyses, and limited data diversity. Therefore, there is a critical need for advanced data-driven frameworks capable of modeling multimodal data to uncover generalizable and biologically meaningful signatures of BED. In this study, we propose the Interpretable Modality-Aware Mixture-of-Experts (IMA-MoE), a novel architecture designed to integrate heterogeneous neuroimaging, behavioral, hormonal, and demographic measures within a unified predictive framework. By encoding each measure as a distinct token, IMA-MoE enables flexible modeling of cross-modal dependencies while preserving modality-specific characteristics. We further introduce a token-importance mechanism to enhance interpretability by quantifying the contribution of each measure to model predictions. Evaluated on the large-scale Adolescent Brain Cognitive Development (ABCD) dataset, IMA-MoE demonstrates superior performance in differentiating BED from healthy controls compared with baseline methods, while revealing sex-specific predictive patterns, with hormonal measures contributing more prominently to prediction in females. Collectively, these findings highlight the promise of interpretable, data-driven multimodal modeling in advancing biologically-informed characterization of BED and facilitating more precise and personalized interventions in neuropsychiatric disorders.