We demonstrate four-wave mixing (FWM) interactions in a-Si:H waveguides in a multilayer integrated silicon photonic chip. The a-Si:H waveguides are accessed through interlayer couplers from waveguides composed of SiNx. The interlayer couplers achieve a coupling of 0.51 dB loss per transition at the target wavelength of 1550 nm. We observe greater idler power extraction and conversion efficiency from the FWM interaction in the interlayer-coupled multilayer waveguides than in single-material waveguides.