Tuberculosis (TB) and lung cancer remain leading causes of mortality worldwide, emphasizing the need for reliable automated diagnostic systems. Existing deep learning approaches typically address segmentation and classification as independent tasks or rely on loosely coupled hybrid architectures, limiting joint optimization and interpretability. To address these limitations, this work proposes a Dual-Path ConvNet–Vision Transformer (ViT) hybrid framework for simultaneous pulmonary disease classification and lesion segmentation. Unlike fully shared multi-task models, the proposed design integrates convolutional feature extraction for classification with transformer-based global context modeling for segmentation, followed by feature-level fusion to enhance diagnostic consistency. The framework is evaluated on the IQ-OTH/NCCD dataset, achieving an accuracy of 0.950, recall of 0.951, precision of 0.947, specificity of 0.975, F1-score of 0.949, and AUC of 0.963. Results demonstrate that the proposed hybrid approach provides robust and interpretable performance for pulmonary disease co-analysis while maintaining architectural flexibility.