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This work delves into unsupervised monocular depth estimation in endoscopy, which leverages adjacent frames to establish a supervisory signal during the training phase. For many clinical applications, e.g., surgical navigation, temporally correlated frames are also available at test time. Due to the lack of depth clues, making full use of the temporal correlation among multiple video frames at both phases is crucial for accurate depth estimation. However, several challenges in endoscopic scenes, such as low and homogeneous textures and inter-frame brightness fluctuations, limit the performance gain from the temporal correlation. To fully exploit it, we propose a novel unsupervised multi-frame monocular depth estimation model. The proposed model integrates a learnable patchmatch module to adaptively increase the discriminative ability in regions with low and homogeneous textures, and enforces cross-teaching and self-teaching consistencies to provide efficacious regularizations towards brightness fluctuations. Furthermore, as a byproduct of the self-teaching paradigm, the proposed model is able to improve the depth predictions when more frames are input at test time. We conduct detailed experiments on multiple datasets, including SCARED, EndoSLAM, Hamlyn and SERV-CT. The experimental results indicate that our model exceeds the state-of-the-art competitors. The source code and trained models will be publicly available upon the acceptance.