The coupling of plasmons and vibrational modes has been routinely observed in graphene and other 2D systems in both near-field and far-field spectroscopy. However, the relation between coupling strength and modal losses, and exceptional point physics has not been discussed. Here we apply a non-Hermitian framework to a model system of molecular layers on graphene and show that the transition point between strong and weak coupling regimes coincides with the exceptional point of non-Hermitian physics. We further show that the exceptional point can be conveniently located by changing the incident angle of the light and the graphene Fermi energy. Finally, we show that enhanced spectral sensitivity is obtained from small changes in molecular film thickness when the system is tuned to the exceptional point.