High-resolution valence band spectra of ultrathin Ag films on Sn/Si(111)√3×√3 show intrinsic splitting of the quantum-well states (QWSs). Especially at low coverages, the QWSs of such a system display delicate coupling characters with the bulk bands from the substrate. The observed QWS splitting agrees well with the result of the theoretical calculation. We found that the splitting originates from an interface with a finite thickness. In addition, the interface also causes a large sp band splitting due to the Umklapp scattering in the Γ−M direction of the Ag(111) surface Brillouin zone.