Heterostructures made of a layer of a cuprate insulator, La 2 CuO 4 , on the top of a layer of a nonsuperconducting cuprate metal, La 1.55 Sr 0.45 CuO 4 , show high-T c interface superconductivity confined within a single CuO 2 plane. Given this extreme quasi-two-dimensional quantum confinement, it is of interest to find out how does interface superconductivity behave when exposed to an external magnetic field. With this motivation, we have performed contactless tunnel diode oscillator-based measurements in pulsed magnetic fields up to 56 T as well as measurements of the complex mutual inductance between a spiral coil and the film in static fields up to 3 T. Remarkably, we observe that interface superconductivity survives up to very high perpendicular fields, in excess of 40 T. In addition, the critical magnetic field H m (T) reveals an upward divergence with decreasing temperature, in line with vortex melting as in bulk superconducting cuprates.