Aims. We present the boomerang-03 experiment, and the maps of the Stokes parameters I, Q, U of the microwave sky obtained during a 14 day balloon flight in 2003. Methods. Using a balloon-borne mm-wave telescope with polarization sensitive bolometers, three regions of the southern sky were surveyed: a deep survey (∼90 square degrees) and a shallow survey (∼750 square degrees) at high Galactic latitudes (both centered at RA 5.5h, Dec −45• ) and a survey of ∼300 square degrees across the Galactic plane at RA 9.1h, dec −47• . All three surveys were carried out in three wide frequency bands centered at 145, 245 and 345 GHz, with an angular resolution of ∼10 . Results. The 145 GHz maps of Stokes I are dominated by Cosmic Microwave Background (CMB) temperature anisotropy, which is mapped with high signal to noise ratio. The measured anisotropy pattern is consistent with the pattern measured in the same region by boomerang-98 and by WMAP. The 145 GHz maps of Stokes Q and U provide a robust statistical detection of polarization of the CMB when subjected to a power spectrum analysis. The amplitude of the detected polarization is consistent with that of the CMB in the ΛCDM cosmological scenario. At 145 GHz, in the CMB surveys, the intensity and polarization of the astrophysical foregrounds are found to be negligible with respect to the cosmological signal. At 245 and 345 GHz we detect ISD emission correlated to the 3000 GHz IRAS/DIRBE maps, and give upper limits for any other non-CMB component. When compared to monitors of different interstellar components, the intensity maps of the surveyed section of the Galactic plane show that a variety of emission mechanisms is present in that region.