We model optical absorption of monolayer and bilayer graphene on hexagonal boron nitride for the case of closely aligned crystal lattices. We show that perturbations with different spatial symmetry can lead to similar absorption spectra. We suggest that a study of the absorption spectra as a function of the doping for an almost completely full first miniband is necessary to extract meaningful information about the moire characteristics from optical absorption measurements and to distinguish between various theoretical proposals for the physically realistic interaction. Also, for bilayer graphene, the ability to compare spectra for the opposite signs of electric-field-induced interlayer asymmetry might provide additional information about the moire parameters.