The paper deals with synthesis of BaTiO??3 (BT) and Co1-xMgxFe2O4 (MCFO) powder via hydroxide coprecipitation route. The nanocomposites containing (X)Co0.7Mg0.3Fe2O4+(1-X) BaTiO??3 (MBT) are prepared for x=0.2, 0.3,0.4,0.5 and 0.6 and sintered at Ts=10750C, 11500C and 12250C. In this paper we report the crystal structure, microstructural analysis, dielectric constant, Complex Impedance Spectroscopy and magnetoelectric properties of MBT composites. It has been observed that increase in ?r in the paraelectric region is prominent for lower frequencies which is attributed to the presence of interfacial polarization at the boundaries between BT and ferrite phases. Here the complex impedance spectroscopy is carried out on the MBT composites to determine various relaxation processes responsible for the dielectric behaviour of the composite. Further the magnetoelectric coefficient ? is observed to decrease with increasing Ts which is associated with the grain growth and occurrence of voids for increasing Ts.