Listen to this:
Father and Mother said it, so often it made Valentine want to scream at them. It isn't the new Peter! It's the old Peter, only smarter!
How smart? Smarter than you, Father. Smarter than you, Mother. Smarter than anybody you have ever met.
But not smarter than me. (9.39-41)
Who is telling us this? Well, notice in that first sentence that the narrator is outside of the characters, including Valentine: the narrator tells us what Val wants. Yes, folks – that would be a third-person narrator.
Now notice that the rest of this section slips inside Val’s own thought process, including that last line – “not smarter than me” – which is Val’s narration. The narrator may be outside of the story, but the narrator totally dips into the thoughts of the characters and shows us what they’re thinking. Because the narrator seems all-knowing, and can drop into the characters' minds, we call that an "omniscient" narrative voice.
Except we don’t hear everyone’s thoughts, so it’s really "limited omniscient" narration. Throughout most of the book, we stay firmly attached to Ender’s mind. Well, more like firmly attached to Ender’s shoulder – we see the things he sees and every once in a while we get to hear what he thinks about them too. We also sometimes hear what other characters are thinking, such as the quote above where the narrator is giving us a glimpse into Val's mind.
Interestingly, we never actually get to see inside Peter’s mind. Think of that: Ender learns to communicate with aliens and we hear how the aliens think about things. But we never really hear what Peter thinks. Same deal with Bonzo.
It seems like that’s a way for Card to keep our sympathy going for certain characters. After all, we never really get on board with Bonzo because we never see the world through his eyes. He might have very good reasons for trying to kill Ender. (Yeah, he probably doesn’t, but still.) Instead of showing us why Bonzo does the mean things he does, all we see are those mean things. (Kind of reminds us of the buggers. Humans think the buggers are evil because they never get a chance to see the invasions from the buggers' perspective.) That’s why we don’t sympathize with Bonzo and we do with Ender.
Also, we’re never sure if Peter is a serious psychopath or just a regular jerk because we never get to learn what he’s thinking. When he threatens to kill his siblings, is he joking or serious? Like Ender, we never know.
Final note: There’s also the way the chapters open, with the military adults discussing Ender. In a way, these sections kind of let us see what’s inside these guys’ heads since these military people share their thoughts pretty openly. Unless, of course, they’re lying to each other. But they wouldn’t lie, would they?