  Interactions between dark matter and dark energy, allowing both conformal and
and disformal couplings, are studied in detail. We discuss the background
evolution, anisotropies in the cosmic microwave background and large scale
structures. One of our main findings is that a large conformal coupling is not
necessarily disallowed in the presence of a general disformal term. On the
other hand, we find that negative disformal couplings very often lead to
instabilities in the scalar field. Studying the background evolution and linear
perturbations only, our results show that it is observationally challenging to
disentangle disformal from purely conformal couplings.
