Well, I'm not too sure, but first one I had to think of was
Blood+. As for the reasons ...
Spoiler (mouse over to view)
First off, the female main character Saya matches your description more or less perfectly, while her male counterpart seems to take only a supporting role so far, but blends smoothly into fights and therefore brings their relationship almost to an equal level during those moments. Aside from this, Sayas nature brings her near your ideal character: She can be inhuman by times, but acts mostly rather determined and keeps her own plans in mind, even if this means to act cruel. Also, the world of Blood is in the beginning quite realistic, there are good elements (your usual people living the usual life) and dark sides - Which can't even be imagined by most people, but are still there and not just some kind of nightmare, so things are more or less well-balanced.
As for the things, that make me a bit unsure: Well, Saya is a vampire and the psycho character may not be to your liking ...
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"It's like love is a bonus in your life. Even without it, I'm just fine. I don't feel like pointlessly searching for it. You don't have to make yourself unhappy." (Ookami Shoujo to Kuro Ouji)
"Why does it rain?" - "To create drama." (Drops (Andou Yuki))
Although the main female lead fits many of your criteria she also violates several of your do not wants possibly fulfilling your hidden depth criteria, now I that I think about it.
