A process for applying alternating layers by chemical vapor deposition comprises the process steps of depositing an adhesion-promoter layer on a substrate and applying a barrier layer. Alternating layers comprising organic and inorganic materials are deposited alternately, and in this process the coating time for application of the adhesion-promoter layer is between 0.05 s and 4.0 s and the coating time for application of the inorganic barrier layer is between 0.1 s and 6.0 s. A composite material is also produced using the process.