Three types of BaTiO₃ core — amorphous nanoshell composite ceramics were processed from the same core-shell powder by standard sintering, spark-plasma sintering and two-step sintering techniques and characterized by XRD, HRSEM and broadband dielectric spectroscopy in the frequency range 10³ – 10¹³ Hz including the THz and IR range. The samples differed by porosity and by the amount of interdiffusion from the cores to shells, in correlation with their increasing porosity. The dielectric spectra were also calculated using suitable models based on effective medium approximation. The measurements revealed a strong dielectric dispersion below the THz range, which cannot be explained by the modeling, and whose strength was in correlation with the degree of interdiffusion. It is assigned to an effect of the interdiffusion layers, giving rise to a strong interfacial polarization. It appears that the high-frequency dielectric spectroscopy is an extremely sensitive tool for detection of any gradient layers and sample inhomogeneities even in dielectric materials with negligible conductivity.