The Ba0.85Ca0.15Zr0.1Ti0.9O3/La0.67Sr0.33MnO3 (BCZT/LSMO) heterostructures were deposited on LaAlO3 (111) substrates through radio-frequency magnetron sputtering technique. Dielectric behaviors as a function of frequency, temperature and magnetic field were investigated. The frequency dependence of dielectric permittivity exhibited apparent relaxation behavior. The corresponding activation energy estimated from Arrhenius plot was 2 meV. Abnormal point at 120 K was detected from the real part of dielectric permittivity vs temperature plot and magnetodielectricity (MD) vs temperature plot simultaneously, which refer to rhombohedral to orthorhombic phase transition in BCZT. A maximum of 20 percent was obtained in MD-temperature pattern, indicating obvious magneto-electric (ME) coupling. The dielectric permittivity relaxation phenomena as well as magneto-dielectric effect can be ascribed to the role of space charges, which arise at interface of BCZT and LSMO owing to lattice mismatch. The dependence of magneto-dielectric on temperature results from the variation of lattice mismatch degree induced by phase transition of BCZT.