  Motivated by a recent experiment by ENS group on the mixture of Bose and
Fermi superfluids (arxiv:1404.2548), we investigate the effective scattering
between a bosonic atom and a molecule(dimer) of fermion atoms. It is found that
the mean-field prediction of the atom-dimer scattering length ($a_{ad}$), as
simply given by the boson-fermion scattering length ($a_{bf}$), generically
fails. Instead, $a_{ad}$ crucially depends on the ratio between $a_{bf}$ and
$a_{ff}$ (the fermion-fermion scattering length), and in addition
log-periodically depends on the three-body parameter. We identify the universal
parameters in characterizing $a_{ad}$ for a wide range of $a_{ff}$ in the
molecular side of the fermion-fermion Feshbach resonance, and further
demonstrate that the atom-dimer many-body system can become unstable against
either phase separation or collapse as tuning $a_{ff}$. Our results have some
implications to the ENS experiment.
