The composite coherence vortices formed by superimposing two parallel, off-axis partially coherent flattened vortex beams are studied in detail. It is shown that the number and position of composite coherence vortices depend on the beam order, relative off-axis distance and coherence parameter, as well as on the free-space relative propagation distance. The “hidden" composite coherence vortex in the partial coherence regime corresponds to its counterpart——the composite optical vortex in the full coherence regime. In the coherent limit the composite coherence vortex evolves into the composite optical vortex.