Sleep quantification and automatic scoring of sleep stages via electroencephalogram (EEG) signals has been a challenge for years. It is crucial to investigate the correlation of brain waves by sleep EEG analysis due to the association between rhythmic oscillations of neuronal activity and neocortical synchronization. Multiscale joint permutation entropy (MJPE) had been proven to be capable of measuring the correlation between time series from the view of multiple time scales and thus can be a promising approach to address the challenge. Instead of simulation, we tested the MJPE method on a widely used open dataset of sleep EEG time series from healthy subjects and found that the correlation index obtained by MJPE had the capability of quantifying the brain wave correlations under different sleep stages, reflecting the typical sleep patterns and indicating the weakened correlation with aging. A higher level of correlation was found as the sleep stage advanced. The findings based on the MJPE results were in accordance with previous studies and existing knowledge in sleep medicine. In the second part of the study, we applied MJPE on sleep EEGs from subjects under pathological conditions (sleep apnea and sleep at high altitude). Likewise, the correlation index also properly revealed their sleep architectures, with consistent trends of the correlation through the nights. The effectiveness and practicability of the MJPE method had been verified on sleep EEGs. Therefore, the MJPE method should be encouraged to be widely used for analyzing large-scale sleep EEGs under various pathological conditions to provide insight into the mechanisms of the sleep process and neuron synchronization.