We have observed an epilayer-thickness-dependent polarity inversion for the growth of CdTe on Sb(Bi)/CdTe(111)B. For films with Sb(Bi) thicknesses of less than 40 A (15 A), the CdTe layer shows a B (Te-terminated) face, but it switches to an A (Cd-terminated) face for thicker layers. On the other hand, a CdTe layer grown on Bi(Sb)/CdTe(111)A always shows the A face regardless of Sb or Bi layer thicknesses. In order to address the observations we have performed ab initio calculations, which suggest that the polarity of a polar material on a nonpolar one results from the binding energy difference between the two possible surface configurations.