Colloids that are partially wetted by two immiscible fluids can become confined to fluid-fluid interfaces. At sufficiently high volume fractions, the colloids may jam and the interface may crystallize. Examples include bicontinuous interfacially jammed emulsion gels (bijels), which were proposed in this study by Stratford et al. [Science 309, 2198 (2005)] as a hypothetical new class of soft materials in which interpenetrating, continuous domains of two immiscible viscous fluids are maintained in a rigid state by a jammed layer of colloidal particles at their interface. We develop a continuum model for such a system that is capable of simulating the long-time evolution. A Navier-Stokes-Cahn-Hilliard model for the macroscopic two-phase flow system is combined with a surface phase-field-crystal model for the microscopic colloidal system along the interface. The presence of colloids introduces elastic forces at the interface between the two immiscible fluid phases. An adaptive finite element method is used to solve the model numerically. Using a variety of flow configurations in two dimensions, we demonstrate that as colloids jam on the interface and the interface crystallizes, the elastic force may be strong enough to make the interface sufficiently rigid to resist external forces, such as an applied shear flow, as well as surface tension induced coarsening in bicontinuous structures.