Low-loss broadband fiber-to-chip coupling is currently challenging for visible-light photonic-integrated circuits (PICs) that need both high confinement waveguides for high-density integration and a minimum feature size above foundry lithographical limit. Here, we demonstrate bi-layer silicon nitride (SiN) edge couplers that have ≤ 4 dB/facet coupling loss with the Nufern S405-XP fiber over a broad optical wavelength range from 445 to 640 nm. The design uses a thin layer of SiN to expand the mode at the facet and adiabatically transfers the input light into a high-confinement single-mode waveguide (150-nm thick) for routing, while keeping the minimum nominal lithographic feature size at 150 nm. The achieved fiber-to-chip coupling loss is about 3 to 5 dB lower than that of single-layer designs with the same waveguide confinement and minimum feature size limitation.