To improve treatment outcomes, lung disorders such as COVID-19, pneumonia, and tuberculosis must be detected quickly and accurately. These illnesses represent major worldwide health concerns. Chest X-ray (CXR) analysis has been greatly improved by developments in deep learning (DL), especially convolutional neural networks (CNNs) and transformer-based models. Although CNNs are excellent at extracting spatial characteristics, transformers are superior at capturing long-range relationships, which increases classification accuracy. Nevertheless, modern methods still have problems with interpretability, model generalization, and class imbalance. DeepDX, a hybrid architecture that incorporates CNNs and transformers, is presented in this work to enhance the multiclass classification of pulmonary illnesses. The architecture maximizes diagnostic accuracy while maintaining transparency by combining ensemble learning, explainable AI (XAI) approaches, and data balance. DeepDX is a useful addition to AI-assisted medical imaging since experimental results on benchmark datasets show that it performs better than current models in terms of accuracy and interpretability.