Monocular 3D detection of vehicle and infrastructure sides are two important topics in autonomous driving. Due to diverse sensor installations and focal lengths, researchers are faced with the challenge of constructing algorithms for the two topics based on different prior knowledge. In this paper, by taking into account the diversity of pitch angles and focal lengths, we propose a unified optimization target named normalized depth, which realizes the unification of 3D detection problems for the two sides. Furthermore, to enhance the accuracy of monocular 3D detection, 3D normalized cube depth of obstacle is developed to promote the learning of depth information. We posit that the richness of depth clues is a pivotal factor impacting the detection performance on both the vehicle and infrastructure sides. A richer set of depth clues facilitates the model to learn better spatial knowledge, and the 3D normalized cube depth offers sufficient depth clues. Extensive experiments demonstrate the effectiveness of our approach. Without introducing any extra information, our method, named MonoUNI, achieves state-of-the-art performance on five widely used monocular 3D detection benchmarks, including Rope3D and DAIR-V2X-I for the infrastructure side, KITTI and Waymo for the vehicle side, and nuScenes for the cross-dataset evaluation.