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In low-temperature resonant Raman experiments on MoSe_{2}-WSe_{2} heterobilayers, we identify a hybrid interlayer shear mode (HSM) with an energy close to the interlayer shear mode (SM) of the heterobilayers, but with a much broader, asymmetric lineshape. The HSM shows a pronounced resonance with the intralayer hybrid trions (HX^{−}) of the MoSe_{2} and WSe_{2} layers only. No resonance with the neutral intralayer excitons is found. First-principles calculations reveal a strong coupling of Q-valley states, which are delocalized over both layers and participate in the HX^{−} with the SM. This emerging trion-phonon coupling may be relevant for experiments on gate-controlled heterobilayers.