Dispersion due to refraction by a prism and dispersion by interference between thin films are completely different, and have almost nothing to do with each other.
They are each wave phenomena, but with different mechanisms.
One very significant difference is that for dispersion to occur in a prism, the index of refraction has to be wavelength dependent. Because of dispersion relations (Kramers-Kronig relations), there has to also be absorption in the prism. See http://en.wikipedia.org/wiki/Kramers–Kronig_relation
Absorption is not required for reflection of different wavelengths (colors) from thin films at different angles.