Hazy images captured under ill-posed scenarios with scattering medium (i.e. haze, fog, or smoke) are contaminated in visibility. Inevitably, these images are further degraded by noises owing to real-world imaging. Most existing hazy image enhancement methods perform image dehazing and denoising stage by stage, with the undesirable result that the estimation error of the former stage has to be propagated and amplified in the latter stage, e.g., noise amplification after dehazing. To address this inconsistent degradation, we present an Unsupervised Unified Image Dehazing and Denoising Network, U²D²Net, to remove the haze and suppress the noise simultaneously for a single hazy image. U²D²Net is mainly comprised of an unsupervised dehazing module, an unsupervised denoising module, and a region-similarity fusion strategy. Specifically, we propose an unsupervised transmission-aware dehazing module to restore visibility and suppress depth-dependent noise propagation in the dehazing module. Besides, we design an unsupervised network with a Mean/Max Sub-Sampler in the denoising module. To exploit the correlation and complementary between the previous outputs, a region-similarity fusion strategy is developed to compute the final qualified result. Extensive experiments on both synthetic and real-world datasets illustrate that U²D²Net outperforms other state-of-the-art dehazing and denoising methods in terms of PSNR, SSIM, and subjective visual effects.