With the progress of 3D human pose and shape estimation, state-of-the-art methods can either be robust to occlusions or obtain pixel-aligned accuracy in non-occlusion cases. However, they cannot obtain robustness and mesh-image alignment at the same time. In this work, we present NIKI (Neural Inverse Kinematics with Invertible Neural Network), which models bi-directional errors to improve the robustness to occlusions and obtain pixel-aligned accuracy. NIKI can learn from both the forward and inverse processes with invertible networks. In the inverse process, the model separates the error from the plausible 3D pose manifold for a robust 3D human pose estimation. In the forward process, we enforce the zero-error boundary conditions to improve the sensitivity to reliable joint positions for better mesh-image alignment. Furthermore, NIKI emulates the analytical inverse kinematics algorithms with the twist-and-swing decomposition for better interpretability. Experiments on standard and occlusion-specific benchmarks demonstrate the effectiveness of NIKI, where we exhibit robust and well-aligned results simultaneously. Code is available at https://github.com/Jeff-sjtu/NIKI