One of the most debated issues about sub-mJy radio sources, which are responsible for the steepening of the 1.4 GHz source counts, is the origin of their radio emission. Particularly interesting is the possibility of combining radio spectral index information with other observational properties to assess whether the sources are triggered by star formation or nuclear activity. The aim of this work is to study the optical and near infrared properties of a complete sample of 131 radio sources with S>0.4 mJy, observed at both 1.4 and 5 GHz as part of the ATESP radio survey. We use deep multi-colour (UBVRIJK) images, mostly taken in the framework of the ESO Deep Public Survey, to optically identify and derive photometric redshifts for the ATESP radio sources. Deep optical coverage and extensive colour information are available for 3/4 of the region covered by the radio sample. Typical depths of the images are U~25, B~26, V~25.4, R~25.5, I~24.3, 19.5<K_s<20.2, J<22.2. Optical/near infrared counterparts are found for ~78% (66/85) of the radio sources in the region covered by the deep multi-colour imaging, and for 56 of these reliable estimates of the redshift and type are derived. We find that many of the sources with flat radio spectra are characterised by high radio-to-optical ratios (R>1000), typical of classical powerful radio galaxies and quasars. Flat-spectrum sources with low R values are preferentially identified with early type galaxies, where the radio emission is most probably triggered by low-luminosity active galactic nuclei. Considering both early type galaxies and quasars as sources with an active nucleus, such sources largely dominate our sample (78%). Flat-spectrum sources associated with early type galaxies are quite compact (d<10-30 kpc), suggesting core-dominated radio emission.
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