  The modified holographic Ricci dark energy coupled to interacting
relativistic and non-relativistic dark matter is considered in the nonflat
Friedmann-Robertson-Walker universe. Through examining the deceleration
parameter, one can find that the transition time of the Universe from
decelerating to accelerating phase in the interacting holographic Ricci dark
energy model is close to that in the $\Lambda$ cold dark matter model. The
evolution of modified holographic Ricci dark energy's state parameter and the
evolution of dark matter and dark energy's densities shows that the dark energy
holds the dominant position from the near past to the future. By studying the
statefinder diagnostic and the evolution of the total pressure, one can find
that this model could explain the Universe's transition from the radiation to
accelerating expansion stage through the dust stage. According to the $Om$
diagnostic, it is easy to find that when the interaction is weak and the
proportion of relativistic dark matter in total dark matter is small, this
model is phantom-like. Through our studying, we find the interaction and the
relativistic dark matter's proportion all have great influence on the evolution
of the Universe.
