Monocular depth estimation (MDE) is a critical task to guide autonomous medical robots. However, obtaining absolute (metric) depth from an endoscopy camera in surgical scenes is difficult, which limits supervised learning of depth on real endoscopic images. Current image-level unsupervised domain adaptation methods translate synthetic images with known depth maps into the style of real endoscopic frames and train depth networks using these translated images with their corresponding depth maps. However a domain gap often remains between real and translated synthetic images. In this paper, we present a latent feature alignment method to improve absolute depth estimation by reducing this domain gap in the context of endoscopic videos of the central airway. Our methods are agnostic to the image translation process and focus on the depth estimation itself. Specifically, the depth network takes translated synthetic and real endoscopic frames as input and learns latent domain-invariant features via adversarial learning and directional feature consistency. The evaluation is conducted on endoscopic videos of central airway phantoms with manually aligned absolute depth maps. Compared to state-of-the-art MDE methods, our approach achieves superior performance on both absolute and relative depth metrics, and consistently improves results across various backbones and pretrained weights. Our code is available at https://github.com/MedICL-VU/MDE.