I'm pretty sure this was on the Playstation, either that or the Nintendo 64. I remember watching someone playing a bit of it my freshman year of college. Fairly primitive graphics by today's standards, but probably pretty decent at the time, blocky polygons and a short draw distance. There was a male protagonist and a female protagonist. I don't remember if you got to choose which one you played, or if it was a "player 1 / player 2" thing, but one was a fairly large man with some sort of polearm, maybe a spear or a trident, and the other was a woman with a sword. I want to say that they both were dressed in somewhat archaic Japanese clothing, but the setting felt more European, with stone-walled buildings. They were fighting demons or monsters of some sort, and I think there was a mixture of outside (city streets) and inside (buildings) stages. I think they also had some magic, but the primary method of fighting was using mêlée weapons.
I think it was at some point ported to the PC, and I picked up a copy (I'll admit, through illicit means, probably Limewire) and didn't get very far in it.
I want to say that the title of the game was two words, something like Strange Creatures... and that actually found me the game. Posting the answer.