Experiments to quantify oxygen diffusion have been performed on polymer samples in which a film of poly(ethylene-co-norbornene) was cast onto a film of polystyrene which, in turn, was cast onto an oxygen-impermeable substrate. In the technique employed, the time evolution of oxygen transport through the film of poly(ethylene-co-norbornene) and into the polystyrene film was monitored using the phosphorescence of singlet oxygen as a spectroscopic probe. To analyze the data, it was necessary to solve Fick's second law of diffusion for both polymer films. Tractable analytical and numerical solutions were obtained for the problem. Moreover, the numerical solution is sufficiently general that it can be used to simulate oxygen concentration profiles in films consisting of more than two layers. Data obtained from the bilayer films yield a diffusion coefficient for oxygen in poly(ethylene-co-norbornene) that is consistent with diffusion coefficients independently obtained from monolayer films and bulk samples.