Self-supervised monocular depth estimation (SSMDE) aims to predict the dense depth map of a monocular image, by learning depth from RGB image sequences, eliminating the need for ground-truth depth labels.Although this approach simplifies data acquisition compared to supervised methods, it struggles with reflective surfaces, as they violate the assumptions of Lambertian reflectance, leading to inaccurate training on such surfaces.To tackle this problem, we propose a novel training strategy for an SSMDE by leveraging triplet mining to pinpoint reflective regions at the pixel level, guided by the camera geometry between different viewpoints.The proposed reflection-aware triplet mining loss specifically penalizes the inappropriate photometric error minimization on the localized reflective regions while preserving depth accuracy on non-reflective areas.We also incorporate a reflection-aware knowledge distillation method that enables a student model to selectively learn the pixel-level knowledge from reflective and non-reflective regions. This results in robust depth estimation across areas.Evaluation results on multiple datasets demonstrate that our method effectively enhances depth quality on reflective surfaces and outperforms state-of-the-art SSMDE baselines.