Superlattices of the repeated structure La_1.56Sr_0.44CuO₄/La₂CuO₄ (LSCO-LCO), where none of the constituents is superconducting, show a superconducting transition of T_c ≃ 25 K. In order to elucidate the nature of the superconducting state we have performed a low-energy μSR study. By applying a magnetic field parallel (Meissner state) and perpendicular (vortex state) to the film planes, we could show that superconductivity is sheet like, resulting in a very anisotropic superconducting state. This result is consistent with a simple charge-transfer model, which takes into account the layered structure and the difference in the chemical potential between LCO and LSCO, as well as Sr interdiffusion. Using a pancake-vortex model we could estimate a strict upper limit of the London penetration depth to 380 nm in these superlattices. The temperature dependence of the muon depolarization rate in field cooling experiments is very similar to what is observed in intercalated BSCCO and suggests that vortex-vortex interaction is dominatedby electromagnetic coupling but negligible Josephson interaction.