The emission properties of most fluorescent emitters, such as dye molecules or solid-state color centers, can be well described by the model of an oscillating electric dipole. However, the orientations of their excitation and emission dipoles are, in most cases, not parallel. Although single molecule excitation and emission dipole orientation measurements have been performed in the past, no experimental method has so far looked at the three-dimensional excitation and emission dipole geometry of individual emitters simultaneously. We present the first experimental study, using defocused imaging in conjunction with radially polarized excitation scanning, to measure both the excitation as well as emission dipole orientations of single molecules, which allows us to sample the distribution of their mutual orientation. We find an unexpectedly broad distribution of the angle between both dipoles which we attribute to the interaction between the observed molecules and the substrate they are immobilized on.