Thanks to deep UV observations with GALEX and Swift, diffuse UV haloes have recently been discovered around galaxies. Based on UV-optical colours, it has been advocated that the UV haloes around spiral galaxies are due to UV radiation emitted from the disc and scattered off dust grains at high latitudes. Detailed UV radiative transfer models that take into account scattering and absorption can explain the morphology of the UV haloes, and they require the presence of an additional thick dust disc next the to traditional thin disc for half of the galaxies in their sample. We test whether such an additional thick dust disc agrees with the observed infrared emission in NGC 3628, an edge-on galaxy with a clear signature of a thick dust disc. We extend the far-ultraviolet radiative transfer models to full-scale panchromatic models. Our model, which contains no fine-tuning, can almost perfectly reproduce the observed spectral energy distribution from UV to mm wavelengths. These results corroborate the interpretation of the extended UV emission in NGC 3628 as scattering off dust grains, and hence of the presence of a substantial amount of diffuse extra-planar dust. A significant caveat, however, is the geometrical simplicity and non-uniqueness of our model: other models with a different geometrical setting could lead to a similar spectral energy distribution. More detailed radiative transfer simulations that compare the model results to images from UV to submm wavelengths are a way to break this degeneracy, as are UV polarisation measurements.