We present an analysis of the propagation properties of a recently introduced class of conjugate mode partially coherent beams (called double-H beams) in a turbulent atmosphere using the extended Huygens-Fresnel integral. We investigate how the phase constant phi(0) between the modes plays a role in controlling the evolution of the intensity distribution and resisting the degradation effects of the atmosphere. Our results indicate that this new class of structured beams provides a new degree of freedom for controlling the shape of the beams and improves turbulence resistance, with potential application in free-space optical communications. (C) 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement