Based on the unified theory of coherence and polarization, the expression for the degree of polarization of partially coherent electromagnetic Hermite-Gaussian (EHG) beams in atmospheric turbulence is derived, and the conditions for keeping polarization invariance are also given. It is shown that the degree of polarization of partially coherent EHG beams in atmospheric turbulence at the observation point (x,y,z) depends on refraction index structure constant of turbulence, coherence length of the source, order numbers of Hermite polynomial, and constant associated with the degree of polarization of the source. However, after a long-propagation distance, the degree of polarization in turbulence tends to the value at the source plane. The result is independent of coherent length and order number of Hermite polynomial, and the strength of turbulence. The change in the polarization of electromagnetic Gaussian Schell-model (EGSM) beams is just a special case of the obtained results.