  We investigate the modal properties of inertial modes of rotating neutron
stars with the core filled with neutron and proton superfluids, taking account
of entrainment effects between the superfluids. In this paper, the entrainment
effects are modeled by introducing a parameter $\eta$ so that no entrainment
state is realized at $\eta=0$. We find that inertial modes of rotating neutron
stars with the superfluid core are split into two families, which we call
ordinary fluid inertial modes ($i^o$-mode) and superfluid inertial modes
($i^s$-mode). The two superfluids in the core counter-move for the $i^s$-modes.
For the $i^o$-modes, $\kappa_0=\lim_{\Omega\to 0}\omega/\Omega$ is only weakly
dependent on the entrainment parameter $\eta$, where $\Omega$ and $\omega$ are
the angular frequency of rotation and the oscillation frequency observed in the
corotating frame of the star, respectively. For the $i^s$-modes, on the other
hand, $|\kappa_0|$ almost linearly increases as $\eta$ increases. Avoided
crossings as functions of $\eta$ are therefore quite common between $i^o$- and
$i^s$-modes. We find that some of the $i^s$-modes that are unstable against the
gravitational radiation reaction at $\eta=0$ become stable when $\eta$ is
larger than $\eta_{crit}$, the value of which depends on the mode. Since the
radiation driven instability associated with the current multipole radiation is
quite weak for the inertial modes and the mutual friction damping in the
superfluid core is strong, the instability caused by the inertial modes will be
easily suppressed unless the entrainment parameter $\eta$ is extremely small
and the mutual friction damping is sufficiently weak.
