In this work, the rational design of optoelectronic properties of two-dimensional materials based on hexagonal boron nitride (h-BN) by functionalization by methyl (CH3) groups is proposed. Using density functional theory, we examine the functionalization of single- or double-layer systems with either CH3 radicals alone or with both CH3 (cations) and chlorine (anions), i.e., under conditions of homolytic or heterolytic splitting of CH3Cl precursor molecules, respectively. Different degrees of methylation (coverages) are considered. The methylation of pure h-BN leads to a reduction of the band gap, while in h-BN/G heterostructures (with methylated graphene layer), methylation increases the band gap. As a consequence, h-BN/G heterostructures offer a high tunability of their optoelectronic properties. To guide possible experiments, vibrational properties and spectra of methylated h-BN and methylated h-BN/G are determined.