This paper focuses on self-supervised monocular depth estimation in dynamic scenes trained on monocular videos. Existing methods jointly estimate pixel-wise depth and motion, relying mainly on an image reconstruction loss. Dynamic regions remain a critical challenge for these methods due to the inherent ambiguity in depth and motion estimation, resulting in inaccurate depth estimation. This paper proposes a self-supervised training framework exploiting pseudo depth labels for dynamic regions from training data. The key contribution of our framework is to decouple depth estimation for static and dynamic regions of images in the training data. We start with an unsupervised depth estimation approach, which provides reliable depth estimates for static regions and motion cues for dynamic regions and allows us to extract moving object information at the instance level. In the next stage, we use an object network to estimate the depth of those moving objects assuming rigid motions. Then, we propose a new scale alignment module to address the scale ambiguity between estimated depths for static and dynamic regions. We can then use the depth labels generated to train an end-to-end depth estimation network and improve its performance. Extensive experiments on the Cityscapes and KITTI datasets show that our self-training strategy consistently outperforms existing self-/unsupervised depth estimation methods.