We analyze visible, infrared, radio and spectroscopic observations of 2060 Chiron in a synthetic way to determine the physical properties of its nucleus. From visible observations performed from 1969 to 2001, we determine an absolute V magnitude for the nucleus of 7.28±0.08 with an amplitude of 0.16±0.03, implying a nearly spherical nucleus with a ratio of semi-axes a/b=1.16±0.03. Infrared observations at 25, 60, 100 and 160 μm (i.e., covering the broad maximum of the spectral energy distribution) obtained with the Infrared Space Observatory Photometer (ISOPHOT) in June 1996 when Chiron was near its perihelion are analyzed with a thermal model which considers an intimate mixture of water ice and refractory materials and includes heat conduction into the interior of the nucleus. We find a very low thermal inertia of 3+5-3 J K-1 m-2 s-1/2 and a radius of 71±5 km. Combining the visible and infrared observations, we derive a geometric albedo of 0.11±0.02. We find that the observed spectra of Chiron can be fitted by a mixture of water ice (̃30%) and refractory (̃ 70%) grains, and that this surface model has a geometric albedo consistent with the above value. We also analyze the visible, infrared and radio observations of Chariklo (1997 CU26) and derive a radius of 118±6 km, a geometric albedo of 0.07±0.01 and a thermal inertia of 0+2-0 J K-1 m-2 s-1/2. A mixture of water ice (̃ 20%) and refractory (̃ 80%) grains is compatible with the near-infrared spectrum and the above albedo.