An unambiguous assignment of the vibrational spectra of ice Ih remains a matter of debate. This study demonstrates that an accurate representation of many-body interactions between water molecules, combined with an explicit treatment of nuclear quantum effects through many-body molecular dynamics (MB-MD), leads to a unified interpretation of the vibrational spectra of ice Ih in terms of the structure and dynamics of the underlying hydrogen-bond network. All features of the infrared and Raman spectra in the OH stretching region can be unambiguously assigned by taking into account both the symmetry and the delocalized nature of the lattice vibrations as well as the local electrostatic environment experienced by each water molecule within the crystal. The high level of agreement with experiment raises prospects for predictive MB-MD simulations that, complementing analogous measurements, will provide molecular-level insights into fundamental processes taking place in bulk ice and on ice surfaces under different thermodynamic conditions.