Atmospheric turbulence (AT) introduces severe degradations, such as rippling, blur, and intensity fluctuations, that hinder both image quality and downstream vision tasks like target detection. While recent deep learning-based approaches have advanced AT mitigation using transformer and Mamba architectures, their high complexity and computational cost make them unsuitable for real-time applications, especially in resource-constrained settings such as remote surveillance. Moreover, the common practice of separating turbulence mitigation and object detection leads to inefficiencies and suboptimal performance. To address these challenges, we propose JDATT, a Joint Distillation framework for Atmospheric Turbulence mitigation and Target detection. JDATT integrates state-of-the-art AT mitigation and detection modules and introduces a unified knowledge distillation strategy that compresses both components while minimizing performance loss. We employ a hybrid distillation scheme: feature-level distillation via Channel-Wise Distillation (CWD) and Masked Generative Distillation (MGD), and output-level distillation via Kullback-Leibler divergence. Experiments on synthetic and real-world turbulence datasets demonstrate that JDATT achieves superior visual restoration and detection accuracy while significantly reducing model size and inference time, making it well-suited for real-time deployment.