Multi-omics integration has demonstrated promising performance in complex disease prediction. However, existing research typically focuses on maximizing prediction accuracy, while often neglecting the essential task of discovering meaningful biomarkers. This issue is particularly important in biomedicine, as molecules often interact rather than function individually to influence disease outcomes. To this end, we propose a two-phase framework named GREMI to assist multi-omics classification and explanation. In the prediction phase, we propose to improve prediction performance by employing a graph attention architecture on sample-wise co-functional networks to incorporate biomolecular interaction information for enhanced feature representation, followed by the integration of a joint-late mixed strategy and the true-class-probability block to adaptively evaluate classification confidence at both feature and omics levels. In the interpretation phase, we propose a multi-view approach to explain disease outcomes from the interaction module perspective, providing a more intuitive understanding and biomedical rationale. We incorporate Monte Carlo tree search (MCTS) to explore local-view subgraphs and pinpoint modules that highly contribute to disease characterization from the global-view. Extensive experiments demonstrate that the proposed framework outperforms state-of-the-art methods in seven different classification tasks, and our model effectively addresses data mutual interference when the number of omics types increases. We further illustrate the functional- and disease-relevance of the identified modules, as well as validate the classification performance of discovered modules using an independent cohort.