Traditional sleep staging categorizes sleep and wakefulness into five coarse-grained classes, overlooking subtle variations within each stage. It provides limited information about the duration of arousal and may hinder research on sleep fragmentation and relevant sleep disorders. To address this issue, we propose a deep learning method for automatic and scalable annotation of continuous sleep depth index (SDI) using existing discrete sleep staging labels. Our approach was validated using polysomnography from over 10,000 recordings across four large-scale cohorts. The results showcased a strong correlation between the decrease in sleep depth index and the increase in duration of arousal. Specific case studies indicated that the sleep depth index captured more nuanced sleep structures than conventional sleep staging. Gaussian mixture models based on the digital biomarkers extracted from the sleep depth index identified two subtypes of sleep, where participants in the disturbed sleep group had a higher prevalence of sleep apnea, insomnia, poor subjective sleep quality, hypertension, and cardiovascular disease. The disturbed subtype was associated with a 42% (hazard ratio 1.42, 95% CI 1.24-1.62) increased risk of mortality and a 29% (hazard ratio 1.29, 95% CI 1.00-1.67) increased risk of fatal cardiovascular disease. Our study underscores the utility of the proposed method for continuous sleep depth annotation, which could reveal more detailed information about the sleep structure and yield novel digital biomarkers for routine clinical use in sleep medicine.