We present the broad-band Spectral Energy Distributions (SEDs) of the largest available highly (72%) complete spectroscopic sample of mid-infrared (MIR) selected galaxies and AGN at intermediate redshift. The sample contains 203 extragalactic sources from the 15-micron survey in the ELAIS-SWIRE field S1, all with measured spectroscopic redshift. Most of these sources have full multi-wavelength coverage from the far-UV to the far-infrared and lie in the redshift range 0.1<z<1.3. Due to its size, this sample allows us for the first time to characterise the spectral properties of the sources responsible for the strong evolution observed in the MIR. Based on SED-fitting technique we have classified the MIR sources, identifying AGN signatures in about 50% of them. This fraction is significantly higher than that derived from optical spectroscopy (~29%) and is due in particular to the identification of AGN activity in objects spectroscopically classified as galaxies. It is likely that in most of our objects, the AGN is either obscured or of low-luminosity, and thus it does not dominate the energetic output at any wavelength, except in the MIR, showing up just in the range where the host galaxy SED has a minimum. The fraction of AGN strongly depends on the flux density, with that derived through the SED-fitting being about 20% at S(15)~0.5-1 mJy and gradually increasing up to 100% at S(15)>10 mJy, while that obtained from optical spectroscopy never being >30%, even at the higher flux densities. The results of this work will be very useful for updating all the models aimed at interpreting the deep infrared survey data and, in particular, for constraining the nature and the role of dust-obscured systems in the intermediate/high-redshift Universe.