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 φ0 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.