  We study a holographic dark energy model in the framework of Brans-Dicke (BD)
theory with taking into account the interaction between dark matter and
holographic dark energy. We use the recent observational data sets, namely SN
Ia compressed Joint Light-Analysis(cJLA) compilation, Baryon Acoustic
Oscillations (BAO) from BOSS DR12 and the Cosmic Microwave Background (CMB) of
Planck 2015. After calculating the evolution of the equation of state as well
as the deceleration parameters, we find that with a logarithmic form for the BD
scalar field the phantom crossing can be achieved in the late time of cosmic
evolution. Unlike the conventional theory of holographic dark energy in
standard cosmology ($\omega_D=0$), our model results a late time accelerated
expansion. It is also shown that the cosmic coincidence problem may be resolved
in the proposed model. We execute the statefinder and Om diagnostic tools and
demonstrate that interaction term does not play a significant role. Based on
the observational data sets used in this paper it seems that the best value
with $1\sigma$ and $2\sigma$ confidence interval are
$\Omega_m=0.268^{+0.008~+0.010}_{-0.007~-0.009}$, $
\alpha=3.361^{+0.332~+0.483}_{-0.401~-0.522}$,
$\beta=5.560^{+0.541~+0.780}_{-0.510~-0.729}$,
$c=0.777^{+0.023~+0.029}_{-0.017~-0.023}$ and $b^2 =0.045$, according to which
we find that the proposed model in the presence of interaction is compatible
with the recent observational data.
