Sleep is essential for maintaining human health and quality of life. Analyzing physiological signals during sleep is critical in assessing sleep quality and diagnosing sleep disorders. However, manual diagnoses by clinicians are time-intensive and subjective. Despite advances in deep learning that have enhanced automation, these approaches remain heavily dependent on large-scale labeled datasets. This study introduces SynthSleepNet, a multimodal hybrid self-supervised learning framework designed for analyzing polysomnography (PSG) data. SynthSleepNet effectively integrates masked prediction and contrastive learning to leverage complementary features across multiple modalities, including electroencephalogram (EEG), electrooculography (EOG), electromyography (EMG), and electrocardiogram (ECG). This approach enables the model to learn highly expressive representations of PSG data. Furthermore, a temporal context module based on Mamba was developed to efficiently capture contextual information across signals. SynthSleepNet achieved superior performance compared to state-of-the-art methods across three downstream tasks: sleep-stage classification, apnea detection, and hypopnea detection, with accuracies of 89.89%, 99.75%, and 89.60%, respectively. The model demonstrated robust performance in a semi-supervised learning environment with limited labels, achieving accuracies of 87.98%, 99.37%, and 77.52% in the same tasks. These results underscore the potential of the model as a foundational tool for the comprehensive analysis of PSG data. SynthSleepNet demonstrates comprehensively superior performance across multiple downstream tasks compared to other methodologies, making it expected to set a new standard for sleep disorder monitoring and diagnostic systems.