In the present paper a theoretical description of the line shapes of frequency modulated noise-immune cavity-enhanced optical heterodyne molecular spectroscopy (NICE-OHMS) under saturated conditions is presented. Expressions for both Doppler broadened and Doppler free frequency modulated NICE-OHMS signals at their absorption and dispersion phases are given. The modulation frequency, saturation parameter and frequency modulation index are set to 384 MHz, 10 and 0.2, respectively in the simulation. Based on the simulated line shape curves, in the absorption detection phase there are four sub Doppler structures existing in the spectral envelope of absorption signals of two sidebands, and in the dispersion phase there are five sub-Doppler structures existing in the spectral envelope of dispersion signals of carrier and two sidebands. The sub-Doppler structure originates from the fact that two counter propagating waves interact with the same group of molecules and one can act as a detecting beam and the other can act as a pumping beam. Therefore the sub-Doppler structure can appear at laser carrier and sidebands frequency and their middle frequencies of carrier and sidebands. Since NICE-OHMS absorption signal is only related to the absorption of sidebands the small saturation parameters of two sidebands can not saturate the Doppler broadened signal too much. Although the NICE-OHMS dispersion signal includes the dispersion of carrier and two sidebands, the amplitude of Doppler broadened signal does not have so much influence by saturation except for the Doppler free signal. Therefore NICE-OHMS technique is a good candidate for the high sensitive detection of gas medium but with high selectivity under the condition of low pressure. Finally the dependences of NICE-OHMS line shape on the detection phase and saturation parameter are simulated and analyzed, the results of which nicely agree with the existing experimental results. The researches on NICE-OHMS line shapes will help explain the phenomena of related experiment.