HD3167 is a bright (V=8.9 mag) K0V star observed by the NASAs K2 space mission during its Campaign 8. It has been recently found to host two small transiting planets, namely, HD3167b, an ultra short period (0.96 d) super-Earth, and HD3167c, a mini-Neptune on a relatively long-period orbit (29.85 d). Here we present an intensive radial velocity follow-up of HD3167 performed with the FIES@NOT, HARPS@ESO-3.6m, and HARPS-N@TNG spectrographs. We revise the system parameters and determine radii, masses, and densities of the two transiting planets by combining the K2 photometry with our spectroscopic data. With a mass of 5.69+/-0.44 MEarth, radius of 1.574+/-0.054 REarth, and mean density of 8.00(+1.0)(-0.98) g/cm^3, HD3167b joins the small group of ultra-short period planets known to have a rocky terrestrial composition. HD3167c has a mass of 8.33 (+1.79)(-1.85) MEarth and a radius of 2.740(+0.106)(-0.100) REarth, yielding a mean density of 2.21(+0.56)(-0.53) g/cm^3, indicative of a planet with a composition comprising a solid core surrounded by a thick atmospheric envelope. The rather large pressure scale height (about 350 km) and the brightness of the host star make HD3167c an ideal target for atmospheric characterization via transmission spectroscopy across a broad range of wavelengths. We found evidence of additional signals in the radial velocity measurements but the currently available data set does not allow us to draw any firm conclusion on the origin of the observed variation.
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