Pretrained Multimodal Large Language Models (MLLMs) are increasingly used in sensitive domains such as medical AI, where privacy regulations like HIPAA and GDPR require specific removal of individuals' or institutions' data. This motivates machine unlearning, which aims to remove the influence of target data from a trained model. However, existing unlearning benchmarks fail to reflect the hierarchical and multimodal structure of real-world medical data, limiting their ability to properly evaluate unlearning in practice. Therefore, we introduce MedForget, a hierarchy-aware multimodal unlearning benchmark that models hospital data as a nested structure, enabling fine-grained evaluation of multimodal unlearning across retain and forget splits. Experiments with current unlearning methods show that existing approaches struggle to achieve effective hierarchy-aware forgetting without degrading downstream medical utility. To address this limitation, we propose Cross-modal Hierarchy-Informed Projection for unlearning (CHIP), a training-free, hierarchy-aware multimodal unlearning method that deletes information by selectively removing target-specific weight subspaces while preserving sibling-shared information. Experiments show that CHIP achieves the highest forget-retain performance gap across all hierarchy levels while maintaining competitive downstream utility compared to existing methods. Overall, MedForget provides a practical, HIPAA-aligned benchmark for evaluating structured multimodal unlearning for medical data, and CHIP offers an effective and general solution for hierarchy-aware forgetting that balances deletion with utility.