We numerically demonstrate that a recently discovered and experimentally realized class of partially coherent Airy beams atop incoherent background remains robust during propagation through a statistically homogeneous isotropic random medium, such as the turbulent atmosphere. We show that these Airy beams on incoherent background, which are propagation-invariant in free space, can mitigate turbulence-induced intensity fluctuations under both weak and strong turbulence conditions. We utilize a pseudo-modal decomposition to numerically model the intensity distribution of these beams, with the results that agree well with analytical predictions. Additionally, we show that, compared to their fully coherent counterparts, Airy beams on incoherent background better preserve their spatial structure under turbulence, making them promising candidates for modern optical communication through atmospheric turbulence.