Three-dimensional linear ray theory is used to investigate internal waves interacting with a Lamb-Chaplygin pancake vortex dipole. These interactions involve waves propagating in the same (co-propagating) and opposite (counter-propagating) horizontal directions as the dipole translation. Co-propagating internal waves in the vertical symmetry plane between the vortices of the dipole can approach critical levels where the wave energy is absorbed by the dipole or where the waves are overturned and possibly break. As wave breaking cannot be simulated with this linear model, changes in wave steepness are calculated to aid in estimating the onset of breaking. Counter-propagating internal waves in the vertical symmetry plane can experience horizontal and vertical reflections, including turning points similar to waves in two-dimensional steady shear. Wave capture is also a possible effect of either type of interaction, depending on initial wave properties and positioning relative to the vortex dipole. Away from the vertical symmetry plane, a spanwise converging (focusing) and diverging (defocusing) of wave energy is observed in co- and counter-propagating interactions as symmetric off-center rays interact with the dipole's individual vortices. Some off-center rays experience multiple horizontal refractions similar to wave trapping.