A theoretical description of Doppler-broadened noise-immune cavity-enhanced optical heterodyne molecular spectroscopy (NICE-OHMS) under optically saturated conditions is presented. Expressions for the strength and shape of the Doppler-broadened NICE-OHMS signals are given for both the absorption and the dispersion phase, in the Voigt regime as well as in the Doppler limit. It is shown that Doppler-broadened NICE-OHMS is affected less by optical saturation than other cavity-enhanced techniques; in the Doppler limit the absorption signal decreases by a factor of $(1+G_{\pm 1}{)}^{-1∕2}$ , where $G_{\pm 1}$ is the degree of saturation for one of the frequency modulation sidebands, whereas the dispersion signal is virtually unaffected by optical saturation. In the Voigt regime both signals show additional dependence on optical saturation. The concept of saturation-insensitive detection is introduced and its conditions are identified.