It is difficult for both cameras and depth sensors to obtain reliable information in hazy scenes. Therefore, image dehazing is still one of the most challenging problems to solve in computer vision and robotics. With the development of convolutional neural networks (CNNs), lots of dehazing and depth estimation algorithms using CNNs have emerged. However, very few of those try to solve these two problems at the same time. Focusing on the fact that traditional haze modeling contains depth information in its formula, we propose a CNN-based simultaneous dehazing and depth estimation network. Our network aims to estimate both a dehazed image and a fully scaled depth map from a single hazy RGB input with end-toend training. The network contains a single dense encoder and four separate decoders; each of them shares the encoded image representation while performing individual tasks. We suggest a novel depth-transmission consistency loss in the training scheme to fully utilize the correlation between the depth information and transmission map. To demonstrate the robustness and effectiveness of our algorithm, we performed various ablation studies and compared our results to those of state-of-the-art algorithms in dehazing and single image depth estimation, both qualitatively and quantitatively. Furthermore, we show the generality of our network by applying it to some real-world examples.