  Coulomb bound electron-hole pairs, excitons, govern the optical properties of
semi-conducting transition metal dichalcogenides like MoS$_2$ and WSe$_2$. We
study optical transitions at the K-point for 2H homobilayer MoS$_2$ in Density
Functional Theory (DFT) including excitonic effects and compare with
reflectivity measurements in high quality samples encapsulated in hexagonal BN.
In both calculated and measured spectra we find a strong interlayer exciton
transition in energy between A and B intralayer excitons, observable for T$=4
-300$ K, whereas no such transition is observed for the monolayer in the same
structure in this energy range. The interlayer excitons consist of an electron
localized in one layer and a hole state delocalized over the bilayer, which
results in the unusual combination of high oscillator strength and a static
dipole moment. We also find signatures of interlayer excitons involving the
second highest valence band (B) and compare absorption calculations for
different bilayer stackings. For homotrilayer MoS$_2$ we also observe
interlayer excitons and an energy splitting between different intralayer
A-excitons originating from the middle and outer layers, respectively.
