A fixed-grid approach for modeling the motion of a particle-encapsulated droplet carried by a pressure-driven immiscible carrier fluid in a microchannel is presented. Three phases (the carrier fluid, the droplet, and the particle) and two different moving boundaries (the droplet-carrier fluid and droplet-particle interfaces) are involved. This is a moving-boundaries problem with the motion of the three phases strongly coupled. In the present article, the particle is assumed to be a fluid of high viscosity and constrained to move with rigid body motion. A combined formulation using one set of governing equations to treat the three phases is employed. The droplet-carrier fluid interface is represented and evolved using a level-set method with a mass-correction scheme. Surface tension is modeled using the continuum surface force model. An additional signed distance function is employed to define the droplet-particle interface. Its evolution is determined from the particle motion governed by the Newton-Euler equations. The governing equations are solved numerically using a finite-volume method on a fixed Cartesian grid. For demonstration purposes, the flows of particle-encapsulated droplets through a constricted microchannel and through a microchannel system are presented.