3D object detection plays a crucial role in numerous intelligent vision systems. Detection in the open world inevitably encounters various adverse scenes, such as dense fog, heavy rain, and low light conditions. Although existing efforts primarily focus on diversifying network architecture or training schemes, resulting in significant progress in 3D object detection, most of these learnable modules fail in adverse scenes, thereby hindering detection performance. To address this issue, this paper proposes a monocular 3D detection model designed to perceive twin depth in adverse scenes, termed MonoTDP, which effectively mitigates the degradation of detection performance in various harsh environments. Specifically, we first introduce an adaptive learning strategy to aid the model in handling uncontrollable weather conditions, significantly resisting degradation caused by various degrading factors. Then, to address the depth/content loss in adverse regions, we propose a novel twin depth perception module that simultaneously estimates scene and object depth, enabling the integration of scene-level features and object-level features. Additionally, we assemble a new adverse 3D object detection dataset encompassing a wide range of challenging scenes, including rainy, foggy, and low light weather conditions, with each type of scene containing 7,481 images. Experimental results demonstrate that our proposed method outperforms current state-of-the-art approaches by an average of 3.12% in terms of AP_R40 for car category across various adverse environments.