If dark energy interacts with dark matter, there is a change in the background evolution of the universe, since the dark matter density no longer evolves as a−3. In addition, the non-gravitational interaction affects the growth of structure. In principle, these changes allow us to detect and constrain an interaction in the dark sector. Here we investigate the growth factor and the weak lensing signal for a new class of interacting dark energy models. In these models, the interaction generalises the simple cases where one dark fluid decays into the other. In order to calculate the effect on structure formation, we perform a careful analysis of the perturbed interaction and its effect on peculiar velocities. Assuming a normalization to today's values of dark matter density and overdensity, the signal of the interaction is an enhancement (suppression) of both the growth factor and the lensing power, when the energy transfer in the background is from dark matter to dark energy (dark energy to dark matter).