"He loved his children." He had never doubted that for a moment. Nor had he doubted that Ned loved him, even though, as he knows now, he's not one of Ned's children. The fact that Ned claimed he was, when he could have just as easily claimed him as a ward instead of a son, is all the convincing Jon needs.

"He and his lady wife even loved each other, even though they were strangers when they married."