A rigorous approach for solving canonical circular open-ended dielectric-lined waveguide diffraction problems is presented. This is continuation of our recent paper (Galyamin et al., 2021) where a simpler case of uniform dielectric filling has been considered. Here we use the same analytical approach based on Wiener-Hopf-Fock technique and deal with more complicated case of a layered dielectric filling which is closer to potential applications. The latter are connected with analytical description of electromagnetic processes involving open-ended waveguide structures prospective due to the modern trends in beam-driven radiation sources (mainly in the terahertz (THz) frequency region) and THz-based bunch manipulation.