We have chosen CaF2/Si(111) as a prototype to study the two‐dimensional band structure of an ordered interface using angle‐resolved photoemission and optical second harmonic generation. A pair of interface state bands is found, one occupied, the other empty. The former disperses fromEF−0.8 eV at Γ toEF−1.4 eV (−1.6 eV) atM(K). An interface band gap of 2.4 eV is determined via resonant second harmonic generation using a truly buried interface with 500 Å of CaF2on top of Si. Therefore, the interfacial gap is twice as large as the gap in Si and five times smaller than the gap in CaF2. The pair of interface bands can be understood as bonding/antibonding combinations of the Si dangling bond orbital and the Ca 4sorbital, with Ca in the 1+oxidation state.