Gravitational Waves (GWs) can determine the luminosity distance of the progenitor directly from the amplitude of the wave, without assuming any specific cosmological model. Thus, it can be considered as a standard siren. The coalescence of binary neutron stars (BNS) or neutron star-black hole pair (NSBH) can generate GWs as well as the electromagnetic counterpart, which can be detected in a form of Gamma-Ray Bursts (GRB) and can be used to determine the redshift of the source. Consequently, such a standard siren can be a very useful probe to constrain the cosmological parameters. In this work, we consider an interacting Dark Matter-Dark Energy (DM-DE) model. Assuming some fiducial values for the parameters of our model, we simulate the luminosity distance for a realistic and optimistic GW+GRB events , which can be detected by the third-generation GW detector Einstein Telescope (ET). Using these simulated events, we perform a Monte Carlo Markov Chain (MCMC) to constrain the DM-DE coupling constant and other model parameters in $1sigma$ and $2sigma$ confidence levels. We also investigate how GWs can improve the constraints obtained by current cosmological probes.