Undoped Mo/Ni superlattices have previously been shown to exhibit a softening of the c44 shear elastic constant with decreasing bilayer thickness. Using ion-beam sputtering, we deposited a series of Mo/Ni superlattice films doped with Al at various concentrations up to 25 at. %. We used Auger electron spectroscopy, x-ray photoelectron spectroscopy, and x-ray diffraction to characterize the chemical and structural properties of the films. The elastic properties of the films were characterized using an improved surface-acoustic-wave (SAW) technique for measuring SAW velocities. We also demonstrate that linear perturbation theory can be used to determine information about the elastic properties of thin films from SAW measurements. We find that the effect of the Al doping on the structural, chemical, and elastic properties of Mo/Ni is small at Al concentrations up to approximately 15 at. %. From Auger bevel-map profiles we find that the Al is segregating to the Ni layers. The ability of the Mo/Ni system to tolerate this high concentration of Al is postulated to result from the formation of Ni3Al, whose structural constants closely match those of Ni. At higher Al concentrations a breakdown of the superlattice structure is accompanied by a rehardening of the c44 stiffness constant.