A sandwich-like laminated composite of TbxDy1-xFe2-y/Pb(Zr, Ti)O3/TbxDy1-xFe2-y is prepared with a bonding method. The experimental study shows that the capacitance of the sample has several resonant peaks in the range of the frequency manipulated, and the resonant points shifte with the increase of applied magnetic field. The impedance of the sample also varies from capacitive to inductive ones at about the resonant point by changing the magnetic field. Giant positive and negative magnetocapacitance effects are observed simultaneously near the resonant frequency. From the constitutive equations of magnet and piezoelectrics involved, the capacitances as functions of frequency and magnetic field were theoretically modeled respectively. The results show that the experimental results are in good agreement with the theoretical ones, suggesting that the magnetocapacitance effect of the layered composite of magnetostriction/ piezoelectric originates from the magnetic field-controlled compliance coefficient of the ferromagnetic phase in the sample.