My quarrel isn't merely with the portrayal of men or women, but the portrayal of their relationships and interaction. It is found throughout Moffat's work, in Coupling and even Jekyll. There is a definite "battle of the sexes" edge to it that was not in the classic series.
River is modern feminism warped beyond belief. She seems constantly out to humiliate men, both sexually and emotionally. In no way would I ever describe Mickey and Rose's, Amy and Rory's or River and The Doctor's relationships as remotely healthy. All feature a woman humiliating a man while the man is expected to just take it. If people think that's alright, or that there is no trend, then so be it. But I strongly disagree.
River isn't "feminism", she's a "psychopath". There IS a big difference. She does what she wants, when she wants, and she doesn't recognize any authority, even the Doctor's.
And no, the Doctor and his companions aren't going to have "healthy" relationships. He's a madman with a box. He picks out people who have problems for various reasons and then gets them into a ton of trouble. He's the ultimate "Peter Pan". Also, healthy relationships are boring and don't make for great drama. And the men don't just "take it". The Doctor needs friends to help keep him in check, and the other guys are jealous because they are worried that they can't compete with the Doctor. He is, essentially, using his companions to keep from being lonely, but in the end, he always loses them.
Why do they punch or slap each other? Because it's what the audience wants and it's funny.
You say you want a "realistic" portrayal of a female companion. So, what is "realistic" if you don't consider a relationship with a strong woman normal?