There is strong evidence that modern humans interbred with Neanderthals and Denisovians.  Shouldn't this mean that all three are of the same spieces and modern human a sub-specie?

Species is both, singular and plural. "Specie" refers to coin money. An important thing to consider is that there are different definitions of species, and virtually none are applicable to all organisms uniformly in a meaningful way. Based on reproductive isolation, it is pretty certain by now that these are not different species. As such Denisovians are also identified as Homo sapiens denisova and Neanderthals have been proposed to be named uniformly as H. sapiens neanderthalensis. But for historic reasons it is probably only slowly changing.