A new class of exact vortex dipole solutions is derived for surface quasigeostrophic (sQG) models. The analysis extends the two-dimensional barotropic modon to fully three-dimensional, continuously stratified flow. Dipole structures exist for a variety of sQG configurations. In particular, the basic dipole propagates counter to the phase speed of linear Rossby waves in the presence of uniform background gradients of the surface potential temperature or planetary vorticity, and reduces to the barotropic Lamb dipole in the limit of a thin sQG layer.