We present a model for the diffuse interstellar dust that explains the observed wavelength-dependence of extinction, emission, linear and circular polarisation of light. The model is set-up with a small number of parameters. It consists of a mixture of amorphous carbon and silicate grains with sizes from the molecular domain of 0.5 up to about 500nm. Dust grains with radii larger than 6nm are spheroids. Spheroidal dust particles have a factor 1.5 - 3 larger absorption cross section in the far IR than spherical grains of the same volume. Mass estimates derived from submillimeter observations that ignore this effect are overestimated by the same amount. In the presence of a magnetic field, spheroids may be partly aligned and polarise light. We find that polarisation spectra help to determine the upper particle radius of the otherwise rather unconstrained dust size distribution. Stochastically heated small grains of graphite, silicates and polycyclic aromatic hydrocarbons (PAHs) are included. We tabulate parameters for PAH emission bands in various environments. They show a trend with the hardness of the radiation field that can be explained by the ionisation state or hydrogenation coverage of the molecules. For each dust component its relative weight is specified, so that absolute element abundances are not direct input parameters. The model is confronted with the average properties of the Milky Way, which seems to represent dust in the solar neighbourhood. It is then applied to four specific sight lines including the reflection nebula NGC2023. For these sight lines, we present linear and circular spectro-polarimetric observations obtained with FORS/VLT. Using prolate rather than oblate grains gives a better fit to observed spectra; the axial ratio of the spheroids is typically two and aligned silicates are the dominant contributor to the polarisation.
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