We measured the ultrafast optical response of metal-dielectric superlattices by broadband all-optical pump-probe spectroscopy. The observed phase of the superlattice mode depends on the probe wavelength, making assignments of the excitation mechanism difficult. Ultrafast x-ray diffraction data reveal the true oscillation phase of the lattice which changes as a function of the excitation fluence. This result is confirmed by the fluence dependence of optical transients. We set up a linear chain model of the lattice dynamics and successfully simulated the broadband optical reflection by unit-cell resolved calculation of the strain-dependent dielectric functions of the constituting materials.