Heavy haze leads to severely degraded visual quality for images, and thus the performance of high level image-based tasks such as object detection is deteriorated. It is necessary and important to design an effective dehazing method for the computer vision system. It is well known that image haze is a function of depth and binocular images can predict the depth. Existing binocular dehazing methods conduct disparity estimation and dehazing jointly to enhance each other. However, a small error in disparity gives rise to a large variation in depth and in the estimation of haze-free images. To alleviate the problem, we propose a plain binocular image dehazing network in this paper, called BidNet, to dehaze both the left and right images simultaneously. BidNet does not explicitly perform disparity estimation that is time-consuming and well-known to be challenging. Instead, we design a stereo transformation module to mine the relationship and correlation between binocular images, making the best of varying information of cross views. Additionally, we design a Stereo Foggy Cityscapes dataset extended from the Foggy Cityscapes dataset for training the proposed BidNet. Extensive experimental results demonstrate that BidNet significantly outperforms the SOTA dehazing methods on the synthetic stereo foggy datasets as well as in real stereo foggy scenes. Experimental results show that jointly dehazing binocular image pairs is mutually beneficial, which is better than only dehazing left images. Furthermore, when applying BidNet to preprocess foggy inputs, large improvements are obtained in the performance of object detection, instance segmentation, semantic segmentation, and stereo-based 3D object detection.