Understanding the underlying physical principles that determine the internal structure of objects at the atomic scale is critical for the advancement of nanoscale science. We have performed synchrotron x-ray diffraction studies to determine the structural properties of smooth Pb films with varying thicknesses of 6 to 18 monolayers deposited on a Si(111) substrate at 110 K. We observe quasibilayer variations in the atomic interlayer spacings of the films consistent with charge density oscillations due to quantum confinement of conduction electrons and surface-interface interference effects. Quantum oscillations in atomic step height are also deduced.