The young PSR B0540-69 (B0540) in the LMC is the only pulsar (except the Crab pulsar) for which a near-UV spectrum has been obtained. However, the absolute flux and spectral index of previously published HST/FOS data are significantly higher than suggested by broadband groundbased UBVRI photometry. Using our ESO/VLT/FORS1 spectral observations and HST/WFPC2 archival images we show that the old HST and new VLT spectral data are >50% contaminated by the Pulsar Wind Nebula (PWN) and that this is the reason for the above mentioned difference. We find that the broadband HST spectrum for the range 3300-8000 A is clearly non- thermal and has a negative spectral index of 1.07(+0.20/-0.19). This is dif- ferent from the almost flat spectrum of the Crab pulsar. The PWN of B0540 shows a clear asymmetry of the surface brightness distribution along the major axis of the PWN torus-like structure with respect to the pulsar position, also seen in Chandra X-ray images. This can be linked to the asymmetry of the surrounding SN ejecta. We find no significant spectral index variation over the PWN. Using HST archival images we estimate the proper motion of B0540 to be 4.9+/-2.3 mas/yr, i.e. a transverse velocity of 1190+/-560 km/s along the southern jet of the PWN. This can make PSR B0540 the third pulsar with a proper motion aligned with the jet axis of its PWN, which poses constraints on pulsar kick models. We discuss the interstellar absorption toward B0540 including the contributions from the Milky Way, LMC and the supernova ejecta, and compare unabsorbed multi- wavelength spectra of B0540 and the Crab pulsar, and their PWNs. Compared with the Crab, B0540 and its PWN show a significant depression in the optical range.
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