Crystalline optical whispering gallery mode resonators made from alkaline earth fluorides can achieve exceptionally large optical finesse, and are used in a variety of applications, from frequency stabilization and narrow linewidth lasers, to low-noise microwave generation or soliton Kerr frequency combs. Here we demonstrate an efficient coupling method to resonators of these materials, which employs photonic integrated waveguides on a chip based on silicon nitride. By converting a mode from silicon nitride to a free-hanging silica waveguide on a silicon chip, coupling to a crystalline resonator is achieved with a high extinction, while preserving a quality factor exceeding 200 million. This compact, heterogeneous integration of ultra-high