We investigate the amount and spatial distribution of interstellar dust in edge-on spiral galaxies, using detailed radiative transfer modelling of a homogeneous sample of 12 galaxies selected from the Calar Alto Legacy Integral Field Area survey. Our automated fitting routine, fitskirt, was first validated against artificial data. This is done by simultaneously reproducing the Sloan Digital Sky Survey g-, r-, i- and z-band observations of a toy model in order to combine the information present in the different bands. We show that this combined, oligochromatic fitting has clear advantages over standard monochromatic fitting especially regarding constraints on the dust properties. We model all galaxies in our sample using a three-component model, consisting of a double-exponential disc to describe the stellar and dust discs and using a Sérsic profile to describe the central bulge. The full model contains 19 free parameters, and we are able to constrain all these parameters to a satisfactory level of accuracy without human intervention or strong boundary conditions. Apart from two galaxies, the entire sample can be accurately reproduced by our model. We find that the dust disc is about 75 per cent more extended but only half as high as the stellar disc. The average face-on optical depth in the V band is 0.76 and the spread of 0.60 within our sample is quite substantial, which indicates that some spiral galaxies are relatively opaque even when seen face-on.