A general microscopic approach of low-energy coupling of individual and collective degrees of freedom is presented. The ingredients of a Bohr-Mottelson unified model description are determined consistently from the Skyrme SIII effective interaction, through the adiabatic limit of the time-dependent Hartree-Fock-Bogoliubov approximation. Three specific aspects are developed: (i) the effect of pairing correlations on adiabatic mass parameters and collective dynamics; (ii) a consistent coupling of collective and individual degrees of freedom to describe odd nuclei and (iii) a study of spectroscopic data in odd-odd nuclei as a test of effective nucleon-nucleon interactions.