  We implement the method developed in [1] to construct the most general
parametrised action for linear cosmological perturbations of bimetric theories
of gravity. Specifically, we consider perturbations around a homogeneous and
isotropic background, and identify the complete form of the action invariant
under diffeomorphism transformations, as well as the number of free parameters
characterising this cosmological class of theories. We discuss, in detail, the
case without derivative interactions, and compare our results with those found
in massive bigravity.
