Carbonaceous dust grains are thought to mediate many important chemical reactions within the interstellar medium (ISM) that would not otherwise proceed, and thus have a significant influence on the chemistry of star-forming regions. Laboratory surface science can approximate the conditions in interstellar space, allowing the study of the physical and chemical behaviour of ices frozen on a carbon surface. In this way, we have applied surface science techniques – temperature programmed desorption (TPD) and reflection-absorption infrared spectroscopy (RAIRS) – to study organic species that have previously been detected in the ISM. Acetaldehyde and dimethyl ether are among many such interstellar complex organic molecules (COMs) of interest, and we compare their behaviour as two oxygen-containing compounds which both exhibit relatively weak intermolecular interactions. For both of these molecules, we investigated the pure ice as well as binary layers and mixtures with water ice, particularly looking at their response to thermal and irradiative (ultraviolet) processing. Analysis of the temperature-dependent desorption of the pure ices also allows for determination of kinetic parameters, including the surface binding energy. These parameters can be applied to models for stellar evolution, potentially informing astronomers about the chemical environment in the vicinity of proto-stars.