In this paper we demonstrate a three-dimensional (3D) photonic integration scheme based on crystalline silicon. We develop a process using SU-8 based adhesive bonding to fabricate vertically stacked, double-layer silicon nanomembranes. A single-layer silicon photonic integrated circuit fabricated on a silicon-on-insulator (SOI) chip and a bare SOI chip are bonded together, followed by removal of the bare SOI chip's silicon substrate and buried oxide layer, to form a silicon nanomembrane as a platform for additional photonic layer. We designed and fabricated subwavelength nanostructure based fiber-to-chip grating coupler on the bonded silicon nanomembrane, and also inter-layer grating coupler for coupling between two silicon nanomembranes. The fiber-to-chip grating coupler has a peak efficiency of -3.9 dB at 1545 nm operating wavelength with transverse-electric (TE) polarization. The inter-layer grating coupler has a peak efficiency of -6.8 dB at 1533 nm operating wavelength with TE polarization. The demonstrated approach serves as a potential solution for 3D photonic integration and novel 3D photonic devices.