The integration of medical imaging and clinical text has enabled the emergence of generalist artificial intelligence (AI) systems for healthcare. However, pervasive biases, such as imbalanced disease prevalence, skewed anatomical region distributions, heterogeneous imaging protocols, and demographic disparities, pose significant challenges to the fairness and reliability of vision-language systems in real-world clinical settings. Here we present BiasCareVL, a bias-aware multimodal learning framework that introduces bias control directly into model design, rather than treating it as a post hoc correction. BiasCareVL incorporates adaptive uncertainty modeling with optional human-in-the-loop refinement to regulate the influence of dominant data patterns and to promote equitable reasoning under distributional imbalance. Trained on 3.44 million samples spanning over 15 imaging modalities, the framework supports diverse clinical tasks, including visual question answering, disease classification, segmentation, and report generation within a unified representation space. Across eight public benchmarks covering dermatology, oncology, radiology, and pathology, BiasCareVL consistently outperforms 20 state-of-the-art methods, with pronounced gains in clinically challenging scenarios, including over 10% accuracy improvement in multi-class skin lesion diagnosis and more than 20% Dice improvement in small tumor segmentation. Furthermore, BiasCareVL achieves diagnostic performance exceeding human accuracy with substantially reduced time requirements when evaluated with board-certified radiologists. By open-sourcing BiasCareVL, we aim to promote a transparent, reproducible, and equitable future for AI in healthcare, paving the way for general-purpose, trustworthy, and clinically reliable AI systems.