The quantized electronic structure in Pb films on Si(111) varies substantially as the film thickness increases. The changes in electronic energy cause the thermal stability of the films to oscillate with an approximate bilayer period. The phase of the oscillations can be controlled by interfacial engineering. Comparison of Pb films prepared on Si(111) terminated by In, Au, and Pb as interfactants reveals a phase reversal. For , films made of odd numbers of atomic layers (5, 7, and 9) are more stable than the even ones. This trend is reversed for the other two cases.