We theoretically investigate the frictional drag induced by the Coulomb interaction between spatially separated massless and massive fermions in the Boltzmann regime and at low temperatures. As a model system, we use a double-layer structure composed of a two-dimensional electron gas (2DEG) and an n-doped graphene layer. We analyze this system numerically and also present analytical formulas for the drag resistivity in the limit of large and small interlayer separation. Both, the temperature and density dependence are investigated and compared to 2DEG-2DEG and graphene-graphene double-layer structures. Whereas the density dependence of the transresistivity for small interlayer separation differs already in the leading order for each of those three structures, we find the leading order contribution of the density dependence in the large interlayer separation limit to exhibit the same density dependence in each case. In order to distinguish between the different systems in the large interlayer separation limit, we also investigate the subleading contribution to the transresistivity. Furthermore, we study the Coulomb drag in a double-layer structure consisting of n-doped bilayer and monolayer graphene, which we find to possess the same qualitative behavior as the 2DEG-graphene system.