It's not uncommon for two related but different species to be capable of interbreeding with viable offspring. That doesn't detract from distinct speciation.
You will find in various sources, the names homo sapiens neanderthalensis and homo neanderthalensis, it would appear Wikipedia prefers the latter, which is of course conclusive.
What a species is, exactly, is the biggest spook in biology.
And if they're not the same species, it presents an interesting problem, as it would mean many humans today aren't 100% the same 'species'...
Taxonomy is not a settled question, and I'm not trying to imply it is. But neanderthals exhibited significantly different traits from humans. There is probably a case to be made that modern homo sapiens are a subspecies of neanderthals and another hominid. Hybridization can (and frequently does) result in new species distinct from the forebear species, after many generations. But speciation doesn't preclude interbreeding.