Understanding modality interaction in multimodal large language models (MLLMs) is central to reliable deployment. We introduce Partial Information Decomposition (PID) as a decision-level framework that separates unique, redundant, and synergistic contributions of sensory and linguistic inputs, beyond representation alignment and outcome-based evaluation. Across vision--language benchmarks, PID reveals recurring modality-use profiles: reasoning and grounding-oriented tasks tend to exhibit high synergy, whereas expert and knowledge-oriented tasks show stronger language-unique reliance. These profiles generalize across model families and predict sensitivity to modality-level interventions. We further extend PID to tri-modal systems with Sensory PID, treating language as a control variable to decompose video--audio information gain. Applied to omni-modal models, Sensory PID reveals a sensory synergy bottleneck dominated by visual information even on audio--visual fusion tasks. Finally, PID-guided reweighting provides initial evidence for improving multimodal reasoning and grounding performance.