The growing adoption of Artificial Intelligence (AI) in medical imaging has elevated the need for models that balance high diagnostic performance with interpretability. This paper presents TransGlass, a Transformer-based glass-box AI framework for chest X-ray disease classification that ensures transparent decision-making. TransGlass aims at improving both the accuracy and explanations of classification over the Vision Transformer (ViT) and Swin Transformer networks as the main goal. The framework uses attention-based visualization methods, including Grad-CAM and SHAP to justify AI prediction. On the CHEXPERT dataset, TransGlass had an AUC-ROC of 0.91 of pneumonia classification and a high recall and explainability in contrast to conventional CNNs. We demonstrate the clinical feasibility of use of TransGlass in interpretable AI-assisted diagnostics, which makes it reliable in a high-stakes medical setting.