In this work we introduce a biologically inspired long-range skip connection for the UNet architecture that relies on the perceptual illusion of hybrid images, being images that simultaneously encode two images. The fusion of early encoder features with deeper decoder ones allows UNet models to produce finer-grained dense predictions. While proven in segmentation tasks, the network's benefits are downweighted for dense regression tasks as these long-range skip connections additionally result in texture transfer artifacts. Specifically for depth estimation, this hurts smoothness and introduces false positive edges which are detrimental to the task due to the depth maps' piece-wise smooth nature. The proposed HybridSkip connections show improved performance in balancing the trade-off between edge preservation, and the minimization of texture transfer artifacts that hurt smoothness. This is achieved by the proper and balanced exchange of information that HybridSkip connections offer between the high and low frequency, encoder and decoder features, respectively. The code and models will be made available in the project page.