We report on the electrical characterization of Ba0.5Sr0.5TiO3/YBa2Cu3O7-delta/LaAlO3 multilayer structure, This structure was fabricated using a pulsed laser deposition technique yielding film thicknesses of 300 nm and 800 nm for the YBa2Cu3O7-delta (YBCO) and the Ba0.5Sr0.5TiO3(BST) films, respectively, A transition temperature T-c=91.5 K was measured for the YBCO film in this structure after deposition of the BST layer. The structure was patterned into parallel plate capacitors with 400x400 mu m gold contacts and YBCO electrodes on top and underneath the BST, respectively. A relative dielectric constant (epsilon(r)) similar to 425 and a loss tangent (tan delta) = 0.040 were measured at 1.0 MHz at 298 K and zero dc voltage (V-dc=0 volts). At 77 K, the dielectric data showed 320 less than or equal to epsilon(r) less than or equal to 360 and tanS=0.036 at V-dc= 0 volts. For 5.0 greater than or equal to V-dc greater than or equal to 3.0 volts epsilon(r) could be varied from 180 to 370. For -5.0 less than or equal to V-dc less than or equal to 3.0 volts, epsilon(r) decreased rapidly with little change in tan delta. The epsilon(r) versus V-dc data suggest that changes in epsilon(r) were affected by electrode space charge layers.