Taking the HermitecoshGaussian（HChG） beam as a typical example, the beamwidth spreading and angular spread of HChG beams propagating through atmospheric turbulence are throughly studied. The relative beamwidth and relative angular spread instead of the beamwidth 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 beamwidth spreading and angular spread of HChG beams are. The angular spread of HChG 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 beamwidth spreading of HChG beams for the case of the propagation distance is sufficiently long. The variation of the relative beamwidth of HChG 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 HermiteGaussian, coshGaussian and Gaussian beams in atmospheric turbulence can be treated as special cases of HChG beams.