We have used noncontact, nondestructive picosecond-ultrasonic techniques to characterize Mo/Si multilayer reflection coatings for extreme ultraviolet (EUV) lithography. Using our alternating-pump technique; we successfully excited and detected the two lowest frequency localized acoustic-phonon surface modes. By measuring their vibration frequencies simultaneously, we can extract the two key parameters for EUV reflector performance: d (bilayer thickness) and Gamma (thickness ratio of Mo layer to the bilayer) of the Mo/Si multilayers. To demonstrate the utility of this technique, we measured the surface-mode frequencies and extracted the values of d and Gamma for six mirrors. Good agreement with the results of at-wavelength EUV reflectometry was found. Damage to coatings caused by the pump and probe laser beams was also studied, and found to be negligible given our data-acquisition time.