Epitaxial bilayered thin films of BaxSr1−xTiO3 (BSTO, x = 0.1 and 0.5)/YBa2Cu3O7−δ (YBCO), with different YBCO film thicknesses, have been grown in situ by pulsed-laser deposition on 1.2° vicinal LaAlO3 substrates. The critical thickness for the transformation of the growth mode in YBCO between two-dimensional (2D) step flow and three-dimensional island is experimentally confirmed to be around 180 nm. As the YBCO-film thickness increases from 145 to 250 nm, the tremendous degradation of the film quality, due to the growth-mode change in YBCO, leads to drastic deterioration in the dielectric properties of BSTO thin films, with severe decrease in the figure of merit factor from 148 to 10 in Ba0.1Sr0.9TiO3/YBCO (at 77 K and 100 kHz) and from 56 to 6 in Ba0.5Sr0.5TiO3/YBCO (at 300 K and 100 kHz). As a result, the dielectric properties of BSTO thin films could be significantly enhanced by strictly tailoring the growth mode in YBCO as a 2D step flow for this kind of BSTO/YBCO bilayers.