What is it with Harry's blood lineage

In every fan-fic I've read that refers to Harry's blood heritage, they call him a half-blood.

Now, Snape and Voldemort and Tonks are half-bloods, having witch mothers and muggle fathers, but Harry's parents are a witch and wizard. Sure, Lily is muggleborn, but she's still a witch. It just seems like the fanon has misinterpreted Harry's bloodlines. What do any of you think about that? Am I wrong? Am I right? Is he a three-quarter blood? Does it not matter? What?

It's just been on my mind lately. Dunno why.

~Mab