Rapid eye movement sleep (REM) is believed to have a binary temporal structure with "phasic" and "tonic" microstates, defined by motoric activity versus quiescence, respectively. However, we observed in mice that the frequency of theta activity (a marker of rodent REM) fluctuates in a non-binary fashion, with the extremes of that fluctuation correlating with phasic-type and tonic-type facial motricity. This demonstrates that phasic and tonic REM rather represent ends of a continuum. These cycles of brain physiology and facial movement occurred at 0.01-0.06 Hz, or infraslow frequencies, and affected cross-frequency coupling and neuronal assembly activity in the neocortex, suggesting network functional impact. We then confirmed that humans also demonstrate non-binary phasic/tonic microstates, with continuous 0.01-0.04 Hz respiratory rate cycles matching the incidence of eye movements. Thus, we discovered a fundamental property of REM, which can yield new insights into our understanding of sleep health.