When modeling hydraulic fractures, it is often necessary to include tightly coupled interactions between fluid-filled fractures and the porous host rock. Further, the numerical scheme must accurately discretize processes taking place both in the rock volume and along growing fracture surfaces. This work describes an effective scheme for handling these challenging numerical issues. Solid deformation and fluid pressure in the host rock are modeled using a mixed finite-element/finite-volume scheme. The continuum formulation is enriched with an assumed enhanced strain (AES) method to represent discontinuities in the displacement field due to fractures. Fractures can be arbitrarily oriented and located with respect to the underlying mesh, and no re-meshing is necessary during fracture propagation. Flow along the fracture is modeled using a locally conservative finite volume scheme. Leak-off coupling allows for fluid exchange between the porous matrix and the fracture. Special attention is paid to accurately representing tip conditions on coarse meshes to ensure accurate prediction of tip propagation velocities. The scheme is validated using analytical solutions for fractures propagating under viscosity, toughness, and leakoff-dominated conditions.