Deep learning has demonstrated strong potential for MRI reconstruction. However, conventional supervised learning requires high-quality, high-SNR references for network training, which are often difficult or impossible to obtain in different scenarios, particularly in low-field MRI. Self-supervised learning provides an alternative by removing the need for training references, but its reconstruction performance can degrade when the baseline SNR is low. To address these limitations, we propose hybrid learning, a two-stage training framework that integrates self-supervised and supervised learning for joint MRI reconstruction and denoising when only low-SNR training references are available. Hybrid learning is implemented in two sequential stages. In the first stage, self-supervised learning is applied to fully sampled low-SNR data to generate higher-quality pseudo-references. In the second stage, these pseudo-references are used as targets for supervised learning to reconstruct and denoise undersampled noisy data. The proposed technique was evaluated in multiple experiments involving simulated and real low-field MRI in the lung and brain at different field strengths. Hybrid learning consistently improved image quality over both standard self-supervised learning and supervised learning with noisy training references at different acceleration rates, noise levels, and field strengths, achieving higher SSIM and lower NMSE. The hybrid learning approach is effective for both Cartesian and non-Cartesian acquisitions. Hybrid learning provides an effective solution for training deep MRI reconstruction models in the absence of high-SNR references. By improving image quality in low-SNR settings, particularly for low-field MRI, it holds promise for broader clinical adoption of deep learning-based reconstruction methods.