We present the application of a unidirectional unsteady coupling between a continuum solver and a three dimensional parallel Direct Simulation Monte Carlo (DSMC) code. Two different problems have been considered: the spherically symmetric expansion of a water vapor cloud into a vacuum and the late stages of a comet impact on the Moon. In both cases, unsteady data pre-computed from a continuum solution are used as input to the DSMC code at a fixed interface. The DSMC results were then compared to the continuum results downstream of the interface in a region of mutual validity in order to validate our approach. The DSMC results for the expansion flow showed good agreement with the analytic solution for the density, velocity and temperature downstream of the interface. Similarly, for the comet impact simulations, the DSMC density agrees well with the solution from the continuum solver, the SOVA hydrocode. A slightly hotter solution is however obtained downstream of the interface using the DSMC code compared to the hydrocode solution.