Silica-based thin-film multilayers are investigated as a means to enhance the effective second-order nonlinearity induced in silica glass structures by corona poling. Structures consisting of phosphorus-doped and undoped silica glass layers exhibit second harmonic generation (SHG) that is higher by an order of magnitude compared to the SHG in bulk silica glass poled under the same conditions. When the poled structure consists of two multilayered stacks separated in space, the stacks exhibit comparable poling-induced nonlinearities. This result suggests that the poling voltage is divided between the two stacks such that simultaneous poling of multiple regions within the sample is realized.