We characterize the transition structure at the Si(100)-SiO2 interface by addressing the inverse ion-scattering problem. We achieve sensitivity to Si displacements at the interface by carrying out ion-scattering measurements in the channeling geometry for varying ion energies. To interpret our experimental results, we generate realistic atomic-scale models using a first-principles approach and carry out ion-scattering simulations based on classical interatomic potentials. Silicon displacements larger than 0.09 Angstrom are found to propagate for three layers into the Si substrate, ruling out a transition structure with regularly ordered O bridges, as recently proposed.