Second-harmonic generation (SHG) is a second-order nonlinear optical process that is not allowed in media with inversion symmetry. However, due to the broken symmetry at the surface, surface SHG still occurs, but is generally weak. We experimentally investigate the surface SHG in periodic stacks of alternating, subwavelength dielectric layers, which have a large number of surfaces, thus enhancing surface SHG considerably. To this end, multilayer stacks of SiO2/TiO2 were grown by Plasma Enhanced Atomic Layer Deposition (PEALD) on fused silica substrates. With this technique, individual layers of a thickness of less than 2 nm can be fabricated. We experimentally show that under large angles of incidence (> 20 degrees) there is substantial SHG, well beyond the level, which can be observed from simple interfaces. We perform this experiment for samples with different periods and thicknesses of SiO2/TiO2 and our results are in agreement with theoretical calculations.