We study the van der Waals interaction between Rydberg alkali-metal atoms with fine structure (n2Lj ; L ≤2 ) and heteronuclear alkali-metal dimers in the ground rovibrational state (X +1Σ ; v =0 , J =0 ). We compute the associated C6 dispersion coefficients of atom-molecule pairs involving 133Cs and 85Rb atoms interacting with KRb, LiCs, LiRb, and RbCs molecules. The obtained dispersion coefficients can be accurately fitted to a state-dependent polynomial O (n7) over the range of principal quantum numbers 40 ≤n ≤150 . For all atom-molecule pairs considered, Rydberg states n S2j and n P2j result in attractive 1 /R6 potentials. In contrast, n D2j states can give rise to repulsive potentials for specific atom-molecule pairs. The interaction energy at the LeRoy distance approximately scales as n-5 for n >40 . For intermediate values of n ≲40 , both repulsive and attractive interaction energies of the order of 10-1000 μ K can be achieved with specific atomic and molecular species. The accuracy of the reported C6 coefficients is limited by the quality of the atomic quantum defects, with relative errors Δ C6/C6 estimated to be no greater than 1% on average.