Polysomnography (PSG) signals are essential for studying sleep processes and diagnosing sleep disorders. Analyzing PSG data through deep neural networks (DNNs) for automated sleep monitoring has become increasingly feasible. However, the limited availability of datasets for certain sleep events often leads to DNNs focusing on a single task with a single-sourced training dataset. As a result, these models struggle to transfer to new sleep events and lack robustness when applied to new datasets. To address these challenges, we propose PSG-MAE, a mask autoencoder (MAE) based pre-training framework. By performing self-supervised learning on a large volume of unlabeled PSG data, PSG-MAE develops a robust feature extraction network that can be broadly applied to various sleep event monitoring tasks. Unlike conventional MAEs, PSG-MAE generates complementary masks across PSG channels, integrates a multichannel signal reconstruction method, and employs a self-supervised inter-channel contrastive learning (ICCL) strategy. This approach enables the encoder to capture temporal features from each channel while simultaneously learning latent relationships between channels, thereby enhancing the utilization of multichannel information. Experimental results show that PSG-MAE effectively captures both temporal details and inter-channel information from PSG signals. When the encoder pre-trained through PSG-MAE is fine-tuned with downstream feature decomposition networks, it achieves an accuracy of 83.7% for sleep staging and 90.45% for detecting obstructive sleep apnea, which highlights the framework's robustness and broad applicability.