Aims. Trans-Neptunian objects (TNOs) are bodies populating the Kuiper belt and they are believed to retain the most pristine and least altered material of the solar system. The Herschel open time key programme entitled "TNOs are Cool: A survey of the transNeptunian region" has been awarded 373 h to investigate the albedo, size distribution and thermal properties of TNOs and Centaurs. Here we focus on the brightest targets observed by both the PACS and SPIRE multiband photometers: the dwarf planet Haumea, six TNOs (Huya, Orcus, Quaoar, Salacia, 2002 UX25, and 2002 TC302), and two Centaurs (Chiron and Chariklo). Methods. Flux densities are derived from PACS and SPIRE instruments using optimised data reduction methods. The spectral energy distribution obtained with the Herschel PACS and SPIRE instruments over 6 bands (centred at 70, 100, 160, 250, 350, and 500 μm), with Spitzer-MIPS at 23.7 and 71.4 μm, and with WISE at 11.6 and 22.1 μm in the case of 10199 Chariklo, has been modelled with the NEATM thermal model in order to derive the albedo, diameter, and beaming factor. For the Centaurs Chiron and Chariklo and for the 1000 km sized Orcus and Quaoar, a thermophysical model was also run to better constrain their thermal properties. Results. We derive the size, albedo, and thermal properties, including thermal inertia and surface emissivity, for the 9 TNOs and Centaurs. Several targets show a significant decrease in their spectral emissivity longwards of ∼300 μm and especially at 500 μm. Using our size estimations and the mass values available in the literature, we also derive the bulk densities for the binaries Quaoar/Weywot (2.18 +0.43 −0.36 g/cm 3 ), Orcus/Vanth (1.53 +0.15 −0.13 g/cm 3 ), and Salacia/Actea (1.29 +0.29 −0.23 g/cm 3 ). Quaoar's density is similar to that of the other dwarf planets Pluto and Haumea, and its value implies high contents of refractory materials mixed with ices.