Multimodal healthcare data contain relational information that extends beyond individual patient observations. Effective clinical outcome prediction therefore requires not only integrating information from multiple modalities, but also modeling the relationships between them. Standard fusion approaches do not explicitly capture these interactions, while existing graph-based approaches typically model only a subset of them. We propose DIGOM (Disentangled Interaction Graphs for Outcome prediction in Multimodal healthcare), a graph-based framework that jointly models three complementary interaction types: Intra-patient cross-modal, Cross-patient same-modal, and Cross-patient cross-modal interactions. DIGOM learns a sparse multiplex graph with disentangled views, each encoding interactions between pairs of modalities across patients. Discrete adjacency matrices with patient-adaptive connectivity are sampled via a differentiable mechanism, enabling end-to-end learning and allowing the model to select informative relationships without imposing a fixed number of neighbors. A regularization objective maintains overall graph sparsity, while message passing integrates this relational context into patient representations for outcome prediction. We evaluate DIGOM on two multimodal healthcare datasets, MIMIC-IV and NIH-TB, across five clinical prediction tasks. DIGOM achieves the highest AUROC on all five tasks while using fewer connections than existing multi-interaction approaches. Ablation studies reveal that each interaction type's contribution varies across tasks, highlighting the need to adapt relational structures per task. DIGOM also demonstrates greater robustness to missing modalities, suggesting learned relationships provide complementary information when modalities are unavailable. Post-hoc analyses further reveal task- and outcome-specific connectivity patterns in the learned graphs.

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