  We evaluate the s-wave interaction of pseudoscalar and vector mesons with
both charm and beauty to investigate the possible existence of molecular $BD$,
$B^*D$, $BD^*$, $B^*D^*$, $B\bar D$, $B^*\bar D$, $B\bar D^*$ or $B^* \bar D^*$
meson states. The scattering amplitude is obtained implementing unitarity
starting from a tree level potential accounting for the dominant vector meson
exchange. The diagrams are evaluated using suitable extensions to the heavy
flavor sector of the hidden gauge symmetry Lagrangians involving vector and
pseudoscalar mesons{, respecting heavy quark spin symmetry}. We obtain bound
states at energies above 7 GeV for $BD$ ($J^P=0^+$), $B^*D$ ($1^+$), $BD^*$
($1^+$) and $B^*D^*$ ($0^+$, $1^+$, $2^+$), all in isospin 0. For $B\bar D$
($0^+$), $B^*\bar D$ ($1^+$), $B\bar D^*$ ($1^+$) and $B^*\bar D^*$ ($0^+$,
$1^+$, $2^+$) we also find similar bound states in $I=0$, but much less bound,
which would correspond to exotic meson states with $\bar b$ and $\bar c$
quarks, and for the $I=1$ we find a repulsive interaction. We also evaluate the
scattering lengths in all cases, which can be tested in current investigations
of lattice QCD.
