Depth estimation from monocular endoscopic images presents significant challenges due to the complexity of endoscopic surgery, such as irregular shapes of human soft tissues, as well as variations in lighting conditions. Existing methods primarily estimate the depth information from RGB images directly, and often surffer the limited interpretability and accuracy. Given that RGB and depth images are two views of the same endoscopic surgery scene, in this paper, we introduce a novel concept referred as ``meta feature embedding (MetaFE)", in which the physical entities (e.g., tissues and surgical instruments) of endoscopic surgery are represented using the shared features that can be alternatively decoded into RGB or depth image. With this concept, we propose a two-stage self-supervised learning paradigm for the monocular endoscopic depth estimation. In the first stage, we propose a temporal representation learner using diffusion models, which are aligned with the spatial information through the cross normalization to construct the MetaFE. In the second stage, self-supervised monocular depth estimation with the brightness calibration is applied to decode the meta features into the depth image. Extensive evaluation on diverse endoscopic datasets demonstrates that our approach outperforms the state-of-the-art method in depth estimation, achieving superior accuracy and generalization. The source code will be publicly available.