Recent experiments have shown a remarkable number of collapse and revival oscillations of the matter-wave coherence of ultracold atoms in optical lattices [Will et al., Nature (London) 465, 197 (2010)]. Using a mean-field approximation to the Bose-Hubbard model, we show that the visibility of collapse and revival interference patterns reveals number squeezing of the initial superfluid state. To describe the dynamics, we use an effective Hamiltonian that incorporates the intrinsic two-body and induced three-body interactions, and we analyze in detail the resulting complex pattern of collapse and revival frequencies generated by virtual transitions to higher bands, as a function of lattice parameters and mean-atom number. Our work shows that a combined analysis of both the multiband, nonstationary dynamics in the final deep lattice and the number squeezing of the initial superfluid state explains important characteristics of optical lattice collapse and revival physics. Finally, by treating the two-and three-body interaction strengths and the coefficients describing the initial superposition of number states as free parameters in a fit to the experimental data, it should be possible to go beyond some of the limitations of our model and obtain insight into the breakdown of the mean-field theory for the initial state or the role of nonperturbative effects in the final-state dynamics.