If you have access to XPS or IR spectrometer the suggestions of Joseph and Andrei are the way to go. If you don't have or you are looking for a quick-and-dirty test: water contact angel.
Put a drop of water on the film. The CA will be 80-90° in the case of PET, around 100° for PE. If you have an oxide coating (no matter if it is SiOx, AlOx, or others) a water drop will have a CA in the range between 40° and about 70°. This is due to adsorbates from the atmosphere. Water will spread (CA < 10°) on a clean oxide surface. You can clean the coating by a thorough flushing with e.g. isopropanol, pure (non-denaturated!) ethanol, aceton. Use a solvent with a low content on non-volatile substances and let it run off the surface rather than letting dry the liquid film.
XPS can't always work because in some cases AlOx is also coated with a protective layer. So I'm interested in FTIR (ATR or transmission) if I can monitor a specific wavelength?
If the XPS has the capability to do sputter depth profiling, then that should work no matter what other coatings. I am not sure IR will do what you want now that you say there are other coatings, but it would certainly be the easiest to try.
No, I am just joking, indeed XPS should have all the requirements for your job, and I would highly recommend XPS as many others in this post! Kind regards, Dirk