Leia was thankful that Han didn't interrupt. Because honestly, if he had, she wouldn't know how to pick up the story. It was hard enough recounting everything that had happened without interruption. She at least had a flow going with the story, even with her pauses. But then came Han's reaction to the news about Vader. Well, she had known it was coming, even so, it still caused her to jump some. But her mind was in a different place so it made sense.
While Han stayed standing, Leia remained sitting. After all, Han had a point. Vader was all about lies and deception, but she also knew the ways of the Force. She knew that you could tell if someone was being truthful. And Luke had seemed so certain, he must have had some sort of proof.
"All I know is what Luke told me... and he was very certain of it. He wouldn't have told me it if it he didn't have proof. I know you don't believe in the Force, but there are ways of using it to know if someone is being truthful... It's how I got him to realize that we're related when I had to tell him..."