Tuberculosis (TB) remains a significant global health challenge, characterized by high incidence and mortality rates on a global scale. With the rapid advancement of computer-aided diagnosis (CAD) tools in recent years, CAD has assumed an increasingly crucial role in supporting TB diagnosis. Nonetheless, the development of CAD for TB diagnosis heavily relies on well-annotated computerized tomography (CT) datasets. Currently, the available annotations in TB CT datasets are still limited, which in turn restricts the development of CAD tools for TB diagnosis to some extent. To address this limitation, we introduce DeepPulmoTB, a CT multi-task learning dataset explicitly designed for TB diagnosis. To demonstrate the advantages of DeepPulmoTB, we propose a novel multi-task learning model, DeepPulmoTBNet (DPTBNet), for the joint segmentation and classification of lesion tissues in CT images. The architecture of DPTBNet comprises two subnets: SwinUnetR for the segmentation task, and a lightweight multi-scale network for the classification task. Furthermore, to enhance the model's capacity to capture TB lesion features, we introduce an improved iterative optimization algorithm that refines feature maps by integrating probability maps obtained in previous iterations. Extensive experiments validate the effectiveness of DPTBNet and the practicality of the DeepPulmoTB dataset.