Excitons in thin layers of semiconducting transition metal dichalcogenides are highly subject to the strongly modified Coulomb electron–hole interaction in these materials. Therefore, they do not follow the model system of a two-dimensional hydrogen atom. We investigate experimentally and theoretically excitonic properties in both the monolayer (ML) and the bilayer (BL) of MoSe2 encapsulated in hexagonal BN. The measured magnetic field evolutions of the reflectance contrast spectra of the MoSe2 ML and BL allow us to determine g-factors of intralayer A and B excitons, as well as the g-factor of the interlayer exciton. We explain the dependence of g-factors on the number of layers and excitation state using first principles calculations. Furthermore, we demonstrate that the experimentally measured ladder of excitonic s states in the ML can be reproduced using the approach with the Rytova–Keldysh potential that describes the electron–hole interaction. In contrast, the analogous calculation for the BL case requires taking into account the out-of-plane dielectric response of the MoSe2 BL.