We used atomic-layer molecular beam epitaxy (ALL-MBE) to synthesize bilayer films of a cuprate metal (La1.65Sr0.45CuO4, LSCO) and a cuprate insulator (La2CuO4, LCO), in which interface superconductivity occurs in a layer that is just one-half unit cell thick. We have studied the magnetic field and temperature dependence of the complex sheet conductance, sigma(omega), of these films, and compared them to kappa-(BEDT-TTF)(2)Cu[N(CN)(2)] Br single crystals. The magnetic field H was applied both parallel and perpendicular to the 2D conducting layers. Experiments have been carried out at frequencies between 23 kHz and 50 MHz using either two-coil mutual inductance technique, or the LC resonators with spiral or rectangular coils. The real and the imaginary parts of the mutual-inductance M(T,omega) between the coil and the sample were measured and converted to complex conductivity. For H perpendicular to the conducting layers, we observed almost identical behavior in both films and kappa-Br single crystals: (i) the transition onset in the inductive response, L-k(-1) (T) occurs at a temperature lower by 2 K than in Re sigma(T), (ii) this shift is almost constant with magnetic field up to 8 T; (iii) the vortex diffusion constant D(T) is exponential due to pinning of vortex cores. These results can be described by the extended dynamic theory of the Berezinski-Kosterlitz-Thouless (BKT) transition and dynamics of bound vortex-antivortex pairs with short separation lengths.