This is a hard one. I find that female writers make their male characters kind of girly and vice versa. Since I usually base my characters on people I know, I always try to imagine(and occasionally ask) how they would respond to different situations. Also, you could have a real person of specific gender read that part (or parts) to see if they think it is gender appropriate behavior.
A good example of this is a female character in a book I just read. She was an assassin, smart ass, ballsy girl but she still fell in love dispite herself and cried when her friend died. Another character from the same book, a male this time was hopelessly in love with the main character and did a lot of whining about it (not manly at all!) but when it came down to it he had a lot of male characteristics like being jealous of his brother and constantly thinking about sex. (Okay, please don't assume I think all men are that way, it was just an example!)
Hope that helps!

Badly gendered? No. Badly developed? Yes.

Backed with sufficient motivation, history, and all the "armwave-armwave" details that make any character believable, your character can be anything. Your character can do anything, but only with sufficient reason to make that action believable.

Or, put another way: You can take a real person who has "atypical" attributes -- but without sufficient characterization that supports those attributes, that real person will not be believable as a character.
Or, as I was once told in a fiction critique group more than 20 years ago, "No child that age speaks like that!"
But I had spoken like that at that age. Did that mean my character should have been believable just because I had based her experiences on my own? No way. I had not presented enough evidence to support her existence.

The first thing I thought of when I saw "men with tits" was Gardner Dozois's 1978 Nebula Award nominee, _Strangers_. And although Joanna Russ's female protagonist didn't have a physical dick per se, the first thing I thought of when I saw "women with dicks" was _The Female Man_(1975), and of course Ursula LeGuin's _The Left Hand of Darkness_ (1969).

Okay, I lied. I thought first of the character Lois in her drag king persona "Max Axel" in Alison Bechdel's _Dykes To Watch Out For_.

If you want to gender-bend, do your research. Find your character's motivations and all the details that will create a well-conceptualized, non-stereotypical person. Bad characterization often relies on gimmicks at the expense of depth. Find the necessary depth, and then find ways to articulate and illustrate it. Don't think about gender -- think about your *character*.