  We theoretically examine a continuity between atomic and molecular Fermi
superfluids in a Bose-Fermi mixture near the Feshbach resonance. Considering a
two-channel model describing the Feshbach resonance between Fermi and Bose
atoms, we have constructed the mean-field framework based on the perturbative
expansion of the Feshbach atom-dimer coupling. The resulting effective
Hamiltonian exhibits not only the continuity between atom-atom to
molecule-molecule Cooper pairings but also becomes equivalent to the
two-band-superconductor model with Suhl-Matthias-Walker type pair-exchange
coupling. We demonstrate how these atomic and molecular Fermi superfluids
coexist within the two-band-like superfluid theory. The pair-exchange coupling
and resulting superfluid gaps are found to be strongly enhanced near the
Feshbach resonance due to the interplay between the infrared singularity of
Bogoliubov phonons and their Landau damping arising from the coupling with
fermions. The pair-exchange coupling can be probed via the observation of the
intrinsic Josephson effect between atomic and molecular superfluids.
