Thin films of carbon-containing materials are found in a pervasive number of applications, ranging from well-established industrial binders and coatings to novel biomedical and optoelectronic devices based on recent advances in nanotechnology. Phase separation through self-assembly gives these films their desirable properties; thus, determining the film structure and understanding its formation are key to unravelling the structure-property relationships. However, determining the morphology of thin, carbon-based films via traditional x-ray and neutron scattering techniques is often difficult due to weak contrast between phases and small scattering volumes. Consequently, standard scattering techniques often require either heavy atom, for x-rays, or deuterium labelling, for neutrons, to locate the various chemical constituents in the structure. Here we develop soft x-ray scattering and reflectometry techniques that allow us to analyze the morphology of thin polymer films whose phase-separated domains are distinguishable without resorting to chemical modification or isotopic labelling. With these techniques, we achieve significant, x-ray energy-dependent contrast between carbon atoms in different chemical environments using soft x-ray resonance at the carbon edge. We demonstrate the use of this contrast mechanism on the phase-separated structure of a model thin polymer film. While the realization of these methods represents a significant advance in our ability to probe the morphology of thin polymer films, we expect that they will also find extensive use in the analysis of other thin, carbon-containing films often found in biological systems and new nanocomposite devices.