Aims. The co-evolution of host galaxies and the active black holes which reside in their centre is one of the most important topics in modern observational cosmology. Here we present a study of the properties of obscured active galactic nuclei (AGN) detected in the CDFS 1 Ms observation and their host galaxies. Methods. We limited the analysis to the MUSIC area, for which deep K-band observations obtained with ISAAC@VLT are available, ensuring accurate identifications of the counterparts of the X-ray sources as well as reliable determination of photometric redshifts and galaxy parameters, such as stellar masses and star formation rates. In particular, we: 1) refined the X-ray/infrared/optical association of 179 sources in the MUSIC area detected in the Chandra observation; 2) studied the host galaxies observed and rest frame colors and properties. Results. We found that X-ray selected (L X > ∼ 10 42 erg s −1 ) AGN show Spitzer colors consistent with both AGN and starburst dominated infrared continuum; the latter would not have been selected as AGN from infrared diagnostics. The host galaxies of X-ray selected obscured AGN are all massive (M * > 10 10 M ) and, in 50% of the cases, are also actively forming stars (1/SSFR < t Hubble ) in dusty environments. The median L/L Edd value of the active nucleus is between 2% and 10% depending on the assumed M BH /M * ratio. Finally, we found that the X-ray selected AGN fraction increases with the stellar mass up to a value of ∼30% at z > 1 and M * > 3 × 10 11 M , a fraction significantly higher than in the local Universe for AGN of similar luminosities.