Aims: The aim of the project is to characterise the two components of the brown dwarf system nearest to the Sun, WISE J104915.57-531906.1 (also called Luhman 16AB) at optical and near-infrared wavelengths. Methods: We obtained high signal-to-noise intermediate-resolution (R ~ 6000-11 000) optical (600-1000 nm) and near-infrared (1000-2480 nm) spectra of each component of Luhman 16AB with the X-Shooter instrument on the Very Large Telescope. Results: We classify the primary and secondary of the Luhman 16 system as L6-L7.5 and T0±1, respectively, in agreement with previous measurements published in the literature. We present measurements of the lithium pseudo-equivalent widths, which appear of similar strength in both components (8.2 ± 1.0 Å for the L and 8.4 ± 1.5 Å for the T component). The presence of lithium (7Li) in both components implies masses lower than 0.06 M⊙, while the comparison with models suggests lower limits of 0.04 M⊙. The detection of lithium in the T component is the first of its kind. Similarly, we assess the strength of other alkali lines (e.g. pseudo-equivalent widths of 6-7 Å for RbI and 4-7 Å for CsI) present in the optical and near-infrared regions and compare with estimates for L and T dwarfs. We also derive effective temperatures and luminosities of each component of the binary: -4.66 ± 0.08 dex and 1305 K for the L dwarf and -4.68 ± 0.13 dex and 1320 K for the T dwarf. According to our radial velocity determinations, the binary does not appear to belong to any of the well-known moving group. Our preliminary theoretical analysis of the optical and J-band spectra indicates that the L- and T-type spectra can be reproduced with a single temperature and gravity but different relative chemical abundances, which strongly affects the spectral energy distribution of L/T transition objects. Based on observations collected at the European Southern Observatory, Chile, under DDT programme 290.C-5200(B) (PI Lodieu).FITS files of the reduced spectra are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/581/A73