  In this work we study the cosmological perturbations in massive bigravity in
the presence of non-minimal derivative couplings. For this purpose we consider
a specific subclass of Horndeski scalar-tensor interactions that live on the
unique composite effective metric. For the viability of the model both metrics
have to be dynamical. Nevertheless, the number of allowed kinetic terms is
crucial. We adapt to the restriction of having one single kinetic term. After
deriving the full set of equations of motion for flat
Friedmann-Lemaitre-Robertson-Walker background, we study linear perturbations
on top of it. We show explicitly that only four tensor, two vector and two
scalar degrees of freedom propagate, one of which being the Horndeski scalar,
while the Boulware-Deser ghost can be integrated out.
