We study a novel interacting dark energy − dark matter scenario where the anisotropic stress of the large-scale inhomogeneities is considered. The dark energy has a constant equation of state and the interaction model produces stable perturbations. The resulting picture is constrained using different astronomical data aiming to measure the impact of the anisotropic stress on the cosmological parameters. Our analyses show that a non-zero interaction in the dark sector is allowed, while a non-interaction scenario is recovered within 68 per cent CL. The anisotropic stress is also constrained to be small, and its zero value is permitted within 68 per cent CL. The dark energy equation of state, wx, is also found to be close to ‘−1’ boundary. However, from the ratio of the CMB TT spectra, we see that the model has a mild deviation from the CDM cosmology, while such deviation is almost forbidden from the CMB TT spectra alone. Although the deviation is not much significant, but from this data, we cannot exclude such deviation. Overall, at the background level, the model is close to the CDM cosmology, while at the level of perturbations, a non-zero but a very small interaction in the dark sector is permitted. Perhaps, a more accurate conclusion can be made with the next generation of surveys. We also found that the region, wx < −1, is found to be effective to release the tension on H0. Finally, from the Bayesian analysis, we find that CDM remains still preferred over the interacting scenarios.