Disclosed is a process for the preparation of multilayered, shaped articles having high transparency and low haze and in which at least one layer contains at least one polyester comprising 2,2,4,4-tetramethyl-1,3-cyclobutanediol and a separate layer which contains a transamidized, homogeneous blend of a least two polyamides. The polyester component and the polyamide component have refractive indices which differ by about 0.006 to about -0.0006. The small difference in the refractive indices enable the incorporation of regrind into one or more of the layers of the article while maintaining high clarity. These articles can exhibit improved excellent barrier properties and good melt processability while retaining excellent mechanical properties. Metal catalysts can be incorporated into one or more layers to impart oxygen-scavenging properties.