In multi-view 3D object detection tasks, disparity supervision over overlapping image regions substantially improves the overall detection performance. However, current multi-view 3D object detection methods often fail to detect objects in the overlap region properly, and the network's understanding of the scene is often limited to that of a monocular detection network. To mitigate this issue, we advocate for applying the traditional stereo disparity estimation method to obtain reliable disparity information for the overlap region. Given the disparity estimates as a supervision, we propose to regularize the network to fully utilize the geometric potential of binocular images, and improve the overall detection accuracy. Moreover, we propose to use an adversarial overlap region discriminator, which is trained to minimize the representational gap between non-overlap regions and overlapping regions where objects are often largely occluded or suffer from deformation due to camera distortion, causing a domain shift. We demonstrate the effectiveness of the proposed method with the large-scale multi-view 3D object detection benchmark, called nuScenes. Our experiment shows that our proposed method outperforms the current state-of-the-art methods.