There's a bit in the first book. And really that doesn't count as a spoiler. Bran sees the 3-eyed crow and follows him, in a dream, to the crypt at Winterfell. There he sees and speaks to his father, who, they found out, has been executed. He tells Maester Luwin of it, and that Hodor will not go down to the crypts, so Osha bears him. He tells Maester that he saw Ned and that Ned was sad, because of something with Jon's mother. And the rest is left to chance.
It is often brought up that Ned was honourable, yet fathered a bastard, and even in the book 1, it is said that Catelyn knew men fathered bastards, that Ned was welcome to what solace he found on campaign, as her attentions were focused on Robb, who was breastfeeding. Yet she expected any bastard would be looked after, but not brought home to be reared among a man's own trueborn children, as Jon was. She accepts it as that the northmen are different.
In the book she heard rumours among her maids, of the Lady Ashara, the sister of Ser Arthur Deyne, the Sword of the Morning, and she knew her husband had slew him, and the Lady had thrown herself off a cliff into the sea. She hears rumours that the Lady had born a child.
She speaks as much to Ned and it was one of the few times he went mental at her, though he never struck her. He asks her where she heard such a tale, and after that she never hears anything again.
But it leaves it all open to interpretation, given Ned's flashbacks and dreams, particularly after his leg is crushed and he lies in the dungeons accused of treason.
Ned remembers meeting Deyne, and those who were with him, and the screams of Lyanna from the Tower of Joy, and her 'bed of blood'. And 'Promise me, Ned.'