Recent breakthroughs in AI are poised to fundamentally enhance our study and understanding of healthcare. The development of an integrated many-to-many framework that leverages multiple data modality inputs for the analytical modeling of multiple medical tasks, is critical for a unified understanding of modern medicine. In this work, we introduce M3H, an explainable Multimodal Multitask Machine Learning for Healthcare framework that consolidates learning from diverse multimodal inputs across a broad spectrum of medical task categories and machine learning problem classes. The modular design of the framework ensures its generalizable data processing, task definition, and rapid model prototyping, applicable to both clinical and operational healthcare settings. We evaluate the M3H framework by validating models trained from four modalities (tabular, time-series, language, and vision) on 41 medical tasks across 4 machine learning problem classes. Our results demonstrate that M3H consistently produces multitask models that outperform canonical single-task models (by 1.1- 37.2%) across 37 disease diagnoses from 16 medical departments, three hospital operation forecasts, and one patient phenotyping task: spanning ML problem classes of supervised binary classification, multiclass classification, regression, and clustering. Additionally, the framework introduces a novel attention mechanism to balance self-exploitation (focus on learning source task), and cross-exploration (encourage learning from other tasks). Furthermore, M3H provides explainability insights on how joint learning of additional tasks impacts the learning of source task using a proposed TIM score, shedding light into the dynamics of task interdependencies. Its adaptable architecture facilitates the customization and integration, establishing it as a robust and scalable candidate solution for future AI-driven healthcare systems.