Purpose: Deep learning has demonstrated strong potential for MRI reconstruction, but conventional supervised learning methods require high-quality reference images, which are often unavailable in practice. Self-supervised learning offers an alternative, yet its performance degrades at high acceleration rates. To overcome these limitations, we propose hybrid learning, a novel two-stage training framework that combines self-supervised and supervised learning for robust image reconstruction. Methods: Hybrid learning is implemented in two sequential stages. In the first stage, self-supervised learning is employed to generate improved images from noisy or undersampled reference data. These enhanced images then serve as pseudo-ground truths for the second stage, which uses supervised learning to refine reconstruction performance and support higher acceleration rates. We evaluated hybrid learning in two representative applications: (1) accelerated 0.55T spiral-UTE lung MRI using noisy reference data, and (2) 3D T1 mapping of the brain without access to fully sampled ground truth. Results: For spiral-UTE lung MRI, hybrid learning consistently improved image quality over both self-supervised and conventional supervised methods across different acceleration rates, as measured by SSIM and NMSE. For 3D T1 mapping, hybrid learning achieved superior T1 quantification accuracy across a wide dynamic range, outperforming self-supervised learning in all tested conditions. Conclusions: Hybrid learning provides a practical and effective solution for training deep MRI reconstruction networks when only low-quality or incomplete reference data are available. It enables improved image quality and accurate quantitative mapping across different applications and field strengths, representing a promising technique toward broader clinical deployment of deep learning-based MRI.