Foundation models (FMs) deployed in real-world tasks such as computer-use agents must integrate diverse modalities. How good are FMs at performing joint reasoning, simultaneously reasoning over multiple modalities, especially when the modalities interact and relate to each other to form cross-modal context? To better understand this problem, we study FMs on cross-modal conflicts: scenarios where conflicting evidence is presented across modalities. This allows us to examine whether FMs prioritize one modality over another or reason jointly to reconcile the conflict. Our experiments reveal that FMs can recognize conflicts in unimodal contexts, composed of a single modality, 90% of the time, but the ratio falls as low as 3% when evidence is split across modalities -- similar observations hold in cross-lingual contexts, composed of multiple languages. We trace this failure to cross-modal attention imbalance, showing that FMs exhibit extreme asymmetry in attention scores, disproportionately prioritizing certain modalities. We show that cross-modal attention imbalance does not go away by simply scaling up multimodal or multilingual datasets blindly, since they lack training examples that explicitly require cross-modal reasoning. We demonstrate that even a simple and scalable method of explicitly combining multiple modalities within each training instance significantly reduces attention imbalance. Reduced attention imbalance directly translates to improved downstream performance on several vision-language benchmarks. Our findings underscore the importance of systematically addressing cross-modal contexts to build reliable foundation models.