In the context of massive (bi-)gravity, non-minimal matter couplings have been proposed. These couplings are special in the sense that they are free of the Boulware-Deser ghost below the strong coupling scale and can be used consistently as an effective field theory. Furthermore, they enrich the phenomenology of massive gravity. We consider these couplings in the framework of bimetric gravity and study the cosmological implications for background and linear tensor, vector, and scalar Previous works have investigated special branches of solutions. Here we perform a complete perturbation analysis for the general background equations of motion, completing previous analyses.