The measurement of the dispersion properties of the coherent medium by using homodyne method based on Mach-Zehnder interferometer is analyzed in theory, and then the dispersion properties of three-level Cs atoms medium in two completely opposite coherent effects, electromagnetically induced transparency and electromagnetically induced absorption, are experimentally measured. The results show that at the atomic resonance center, the signal light can pass through the medium due to reduced absorption for the electromagnetically induced transparency medium, which ensure the measurement to the effective dispersion properties information, namely normal dispersion. On the contrary, for the electromagnetically induced absorption medium, due to the strong absorption effect, only at the low atomic densities, i.e. to ensure the signal light through the medium without being fully absorbed, the anomalous dispersion properties of the medium can be measured. Furthermore, when increasing the atomic number density, the absorption of atoms to signal light is enhanced to full absorption, and the absorption spectrum width is widened, which leads to the fact that phase shift can not be effectively measured.