Context. Empirical libraries of stellar spectra are used to classify stars and synthetize stellar populations. MILES is a medium spectral-resolution library in the optical domain covering a wide range of temperatures, surface gravities and metallicities. Aims: We redetermine the atmospheric parameters of these stars in order to improve the homogeneity and accuracy. We build an interpolating function that returns a spectrum as a function of the three atmospheric parameters, and finally we characterize the precision of the wavelength calibration and stability of the spectral resolution. Methods: We used the ULySS program with the ELODIE library as a reference and compared the results with those in the literature. Results: We obtain precisions of 60 K, 0.13, and 0.05 dex, respectively, for Teff, log g, and [Fe/H] for the FGK stars. For the M stars, the mean errors are 38 K, 0.26, and 0.12 dex and 3.5%, 0.17, and 0.13 dex for the OBA. We construct an interpolator that we test against the MILES stars themselves. We test it also by measuring the atmospheric parameters of the CFLIB stars with MILES as reference and find it to be more reliable than the ELODIE interpolator for the evolved hot stars, like those of the blue horizontal branch in particular. FITS files are only and Table 1 also available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/531/A165