Resonant quantum tunneling of magnetization has been observed in a hybrid metal-organic framework where an intrinsic magnetic phase separation leads to the coexistence of long-range canted antiferromagnetic order and isolated single-ion quantum magnets. This unusual magnetic phenomenon is well interpreted based on a selective long-distance superexchange model in which the exchange interaction between transition metal ions through an organic linker depends on the position of hydrogen bonds. Our work not only extends the resonant quantum tunneling of magnetization to a new class of materials but also evokes the important role of hydrogen bonding in organic magnetism.