The microscopic approach for the description of low-lying intrinsic states in deformed odd-odd nuclei is formulated as a generalization of the quasiparticle-phonon model. In comparison with other models used for deformed odd-odd nuclei, the approach proposed in this paper involves vibrational degrees of freedom of the doubly-even core, their coupling to quasiparticle degrees of freedom and the n-p interaction between the odd particles. Our model treats all of these modes of nuclear motion on the same microscopic footing. This proposed model is applied to calculate the energies and phononquasiparticle structure of the intrinsic states of the oddodd Ho isotopes with A = 160, 162, 164, 166 and 168. It is found that the low-lying intrinsic states in the odd-odd Ho isotopes have only small vibrational components. In general the vibrational states are fragmented over many intrinsic states.