A hideously ugly man who pretends to be straight but is definitely gay, and absolutely hopeless at hiding it.
Usually, a Two Face is an ugly arrogant male who acts as if he is God's gift to women.
When, after several hundred rejections, he realises that he is actually not attractive to the opposite gender. He secretly becomes aroused by other men, but panics and wishes to hide this fact from the general public. He visits gay bars at night, and acts generally like one straight person during the day and his gay counterpart at night.
Unfortunately, the Two Face is hopeless at keeping his secret, and constantly overdoes the straight act/lets gay things slip until all his friends want to pull him out the closet for him, and ram The Truth where the sun don't shine.
E.g 1) Guy 1 - "Hey check out that that guy over there, he is so gay."
Guy 2 - "What, HIM? But he seems so straight!"
Guy 1 - "Uhuh, TOO straight. We saw him visiting the Manhole Bar saturday night."
Guy 2 - "Gah, what a Two Face!!!!!"
E.g 2) Girl - "Wanna come back to my place?"
Two Face Guy (loudly to friends) "Aw hell yeah bitch I'mma fuck yo ass yeahhhh I'm a playa bitch I LOVE THE COCK
*Bar goes silent, everyone stares*
Two Face Guy - "..I meant pussy, bitch..aheh.."