In the Books, NO ONE knows the truth of john snow's parrents. Whenever anyone asks Ned about John, he simply shuts up, and stares off. Robert THINKS he knows who the mother is, but Ned refuses to talk about it. NOW, whenever we're in first person persctive inside Ned's head and someone mentions Bastards, or John, Ned's thougths turn to on of a few things.
1) His sister and his deathbed promise to her
2) the butchery of the Targerian children Commited by Tywin lanaster .
so, it's VERY Heavily handed hinting that John is actualy the Son of Ned's sister and Rhaegar Targaryen. Making John the Legetimate Hier to the Iron throne, and Danyeris's nephew.
Ned was never unfaithful. It's NOT in his character.
I rescend my earlier comment. Ned Stark IS the hero of Game of thrones... and it gets him killed.