Single image dehazing is a challenging task, for which the domain shift between synthetic training data and real-world testing images usually leads to degradation of existing methods. To address this issue, we propose a novel image dehazing framework collaborating with unlabeled real data. First, we develop a disentangled image dehazing network (DID-Net), which disentangles the feature representations into three component maps, i.e. the latent haze-free image, the transmission map, and the global atmospheric light estimate, respecting the physical model of a haze process. Our DID-Net predicts the three component maps by progressively integrating features across scales, and refines each map by passing an independent refinement network. Then a disentangled-consistency mean-teacher network (DMT-Net) is employed to collaborate unlabeled real data for boosting single image dehazing. Specifically, we encourage the coarse predictions and refinements of each disentangled component to be consistent between the student and teacher networks by using a consistency loss on unlabeled real data. We make comparison with 13 state-of-the-art dehazing methods on a new collected dataset (Haze4K) and two widely-used dehazing datasets (i.e., SOTS and HazeRD), as well as on real-world hazy images. Experimental results demonstrate that our method has obvious quantitative and qualitative improvements over the existing methods.