Partially coherent phonon transport has been experimentally observed in superlattices. In this paper, a holistic treatment of partially coherent phonon transport is proposed and an interfering Monte Carlo (IMC) method is developed. The IMC method is based on the conventional Monte Carlo (MC) method, but with a particle model that has amplitude and phase information. As such, in addition to diffuse scatterings, wave interference between coherent phonons can also be modeled, resulting in a method that is capable of modeling both particle and wave behavior of the phonons. Numerical study of the cross-plane heat conduction in silicon/heavy silicon superlattices shows that the IMC is able to reproduce the conventional MC results in cases when particle behavior dominates. For cases when wave effects become important, the IMC can also capture wave phenomena that have been experimentally observed or revealed in molecular dynamics simulations. (C) 2016 Elsevier Ltd. All rights reserved.