We constrain interacting dark matter and dark energy (IDMDE) models using a 450-degree-square cosmic shear data from the Kilo Degree Survey (KiDS) and the angular power spectra from Planck's latest cosmic microwave background measurements. We revisit the discordance problem in the standard Lambda cold dark matter (ΛCDM) model between weak lensing and Planck datasets and extend the discussion by introducing interacting dark sectors. The IDMDE models are found to be able to alleviate the discordance between KiDS and Planck as previously inferred from the ΛCDM model, and moderately favored by a combination of the two datasets.