Ok, I have a theory of what the Demons and Angels are like in the New DmC game.
You see, since Dante is clear to be seen by humans and demons, could it be possible that an angel (in DmC) isn't really an angel from the bible? Maybe an angel is like, what they call a human who has the ability to kill demons. Perhaps an angel is like this Holy Warrior whose duty is to defend the people from the demons who are controlling humanity (like the Grey Wardens from Dragon Age). This would make sense how Dante can be seen by humans and demons and yet the humans themselves cannot see the demons.
Could it be possible that an angel is actually some type of ancient warrior destined to face the demons? I don't know, I'm wondering that, I don't know if this is true but if it were true, it would make sense. What do you guys think of this?