Core-shell composites of ferromagnetic conducting nanoparticles La0.65Sr0.35MnO3 (LSMO) embedded in an insulating matrix of TiO2 (LSMO@TiO2) have been processed, structurally and magnetically characterized, and their DC magnetoresistivity and complex dielectric response measured and fitted from Hz up to the infrared (IR) range (1014 Hz). XRD indicates that the TiO2 shells are amorphous. Modelling of the IR spectra using standard models based on the effective medium approximation has it confirmed and has characterized the effective phonon modes of the LSMO nanoceramics and LSMO@TiO2 composite. Modelling of the lower-frequency spectra has shown that TiO2 shell thicknesses are rather non-uniform down to thin nm values, which leads to giant low-frequency permittivity values and non-negligible free-carrier tunnelling among the LSMO cores. Two main dielectric dispersion regions were observed and shown to be due to the inhomogeneous conductivity-the one occuring in the 1011-1012 Hz range relates to nonmagnetic less-conducting dead layers on the surface of LSMO nanocrystallites and the broad second one below the 1010 Hz range is due to the non-uniform thicknesses of the dielectric TiO2 shells. In the IR range, effective phonon modes of the LSMO nanoceramics and LSMO@TiO2 composite were characterized from the reflectivity spectra.