  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.
