Taking the HermitecoshGaussian（HChG） beam as a typical example, the beamwidth spreading and angular spread of HChG beams propagating through atmospheric turbulence are throughly studied. The relative beamwidth and relative angular spread instead of the beamwidth and angular spread have been used to study the sensitivity of a beam to the effect of turbulence. It is found that the smaller the refraction index structure constant C2n is, the less the beamwidth spreading and angular spread of HChG beams are. The angular spread of HChG beams with larger beam orders m, n, smaller parameter Ω0 and smaller waist width w0 is less affected by turbulence. This conclusion also holds true for the beamwidth spreading of HChG beams for the case of the propagation distance is sufficiently long. The variation of the relative beamwidth of HChG beams versus Ω0 and w0 is analyzed if the propagation distance being not so long. The results are illustrated by numerical examples and the validity of the results is explained physically. The spreading of HermiteGaussian, coshGaussian and Gaussian beams in atmospheric turbulence can be treated as special cases of HChG beams.