  We present a specific heat and inelastic neutron scattering study in magnetic
fields up into the 1/3 magnetization plateau phase of the diamond chain
compound azurite Cu$_3$(CO$_3$)$_2$(OH)$_2$. We establish that the
magnetization plateau is a dimer-monomer state, {\it i.e.}, consisting of a
chain of $S = 1/2$ monomers, which are separated by $S = 0$ dimers on the
diamond chain backbone. The effective spin couplings $J_{mono}/k_B = 10.1(2)$ K
and $J_{dimer}/k_B = 1.8(1)$ K are derived from the monomer and dimer
dispersions. They are associated to microscopic couplings $J_1/k_B = 1(2)$ K,
$J_2/k_B = 55(5)$ K and a ferromagnetic $J_3/k_B = -20(5)$ K, possibly as
result of $d_{z^2}$ orbitals in the Cu-O bonds providing the superexchange
pathways.
