We employ a recent formulation for the optical properties of two-dimensional crystals from first principles [L. Matthes, New J. Phys. 16, 105007 (2014)NJOPFM1367-263010.1088/1367-2630/16/10/105007; L. Matthes, Phys. Rev. B 94, 205408 (2016)2469-995010.1103/PhysRevB.94.205408] to compute the surface susceptibility and surface conductivity of MoS2 and WSe2 monolayers [G. Jayaswal, Opt. Lett. 43, 703 (2018)OPLEDP0146-959210.1364/OL.43.000703]. As electron-hole interactions are known to be crucial for the description of the absorption spectrum of monolayer transition metal dichalcogenides, the excitonic dielectric function is computed at the Bethe-Salpeter equation level, including spin-orbit interactions. For both of these examples, excellent agreement with experimental ellipsometry measurements is obtained. Driven by the emergence of additional features in our theoretical results, we applied a second-derivative analysis in order to identify excited exciton peaks in the ellipsometric spectra.