We designed and demonstrated a tri-layer Si3N4/SiO2 photonic integrated circuit capable of vertical interlayer coupling with arbitrary splitting ratios. Based on this multilayer photonic integrated circuit platform with each layer thicknesses of 150 nm, 50 nm, and 150 nm, we designed and simulated the vertical Y-junctions and 3D couplers with arbitrary power splitting ratios between 1:10 and 10:1 and with negligible(< -50 dB) reflection. Based on the design, we fabricated and demonstrated tri-layer vertical Y-junctions with the splitting ratios of 1:1 and 3:2 with excess optical losses of 0.230 dB. Further, we fabricated and demonstrated the 1 × 3 3D couplers with the splitting ratio of 1:1:4 for symmetric structures and variable splitting ratio for asymmetric structures.