  The system of Bose-Fermi superfluid mixture offers a playground to explore
rich macroscopic quantum phenomena. In a recent experiment of Yao {\it et al.}
[Phys. Rev. Lett. {\bf 117}, 145301 (2016)], $^{41}$K-$^{6}$Li superfluid
mixture is implemented. Coupled quantized vortices are generated via rotating
the superfluid mixture, and a few unconventional behaviors on the formations of
vortex numbers are observed, which can be traced to boson-fermion interactions.
Here we provide a theoretical insight into the unconventional behaviors
observed in the experiment. To this end, the orbital-free density functional
theory is hired, and its utility is validated by making comparison of the
numerical results and a microscopic theory for vortex lattices in strongly
interacting Fermi superfluids alone. We also predict interesting phenomena
which can be readily explored experimentally, including the novel structures of
bosonic-fermionic vortices, and attractive interactions between the bosonic and
fermionic vortices.
