The elastic properties of two-component bilayer membranes are studied using a coarse-grain model for amphiphilic molecules. The two species of amphiphiles considered here differ only in their length. Molecular-dynamics simulations are performed in order to analyze the shape fluctuations of the two-component bilayer membranes and to determine their bending rigidity. Both the bending rigidity and its inverse are found to be nonmonotonic functions of the mole fraction xB of the shorter B-amphiphiles and, thus, do not satisfy a simple lever rule. The intrinsic area of the bilayer also exhibits a nonmonotonic dependence on xB and a maximum close to xB simeq 1/2.