Infrared unmanned aerial vehicle (UAV) images captured using thermal detectors are often affected by temperature-dependent low-frequency nonuniformity, which significantly reduces the contrast of the images. Detecting UAV targets under nonuniform conditions is crucial in UAV surveillance applications. Existing methods typically treat infrared nonuniformity correction (NUC) as a preprocessing step for detection, which leads to suboptimal performance. Balancing the two tasks while enhancing detection-beneficial information remains challenging. In this paper, we present a detection-friendly union framework, termed UniCD, that simultaneously addresses both infrared NUC and UAV target detection tasks in an end-to-end manner. We first model NUC as a small number of parameter estimation problem jointly driven by priors and data to generate detection-conducive images. Then, we incorporate a new auxiliary loss with target mask supervision into the backbone of the infrared UAV target detection network to strengthen target features while suppressing the background. To better balance correction and detection, we introduce a detection-guided self-supervised loss to reduce feature discrepancies between the two tasks, thereby enhancing detection robustness to varying nonuniformity levels. Additionally, we construct a new benchmark composed of 50,000 infrared images in various nonuniformity types, multi-scale UAV targets and rich backgrounds with target annotations, called IRBFD. Extensive experiments on IRBFD demonstrate that our UniCD is a robust union framework for NUC and UAV target detection while achieving real-time processing capabilities. Dataset can be available at https://github.com/anonymous2025submit/UniCD.