The permeability of oleic and acetic acid through low density polyethylene (LDPE) and ethylene acrylic acid (EAA) have been measured using diffusion cells. In addition, the permeability through combinations of LDPE and EAA in the form of laminates with different numbers of layers has been determined. Oleic acid shows an almost 30 times higher permeability compared to acetic acid, which was partly explained by the adsorption of oleic acid to the film surface during the permeability experiment. In addition, the permeability is lower for both oleic and acetic acid in the laminates compared to the pure films. The decreased permeability can be explained by the presence of crystalline domains close to the interface. This is supported by SAXS data which suggests an ordering of polymer chains in the EAA film close to the interface. In summary, the results show that it is possible to create barrier materials with decreased permeability, which is interesting for example in the packaging industry.