Accurate and efficient dense metric depth estimation is crucial for 3D visual perception in robotics and XR. In this paper, we develop a monocular visual-inertial motion and depth (VIMD) learning framework to estimate dense metric depth by leveraging accurate and efficient MSCKF-based monocular visual-inertial motion tracking. At the core the proposed VIMD is to exploit multi-view information to iteratively refine per-pixel scale, instead of globally fitting an invariant affine model as in the prior work. The VIMD framework is highly modular, making it compatible with a variety of existing depth estimation backbones. We conduct extensive evaluations on the TartanAir and VOID datasets and demonstrate its zero-shot generalization capabilities on the AR Table dataset. Our results show that VIMD achieves exceptional accuracy and robustness, even with extremely sparse points as few as 10-20 metric depth points per image. This makes the proposed VIMD a practical solution for deployment in resource constrained settings, while its robust performance and strong generalization capabilities offer significant potential across a wide range of scenarios.