Harry's Lineage

[Shell]

No: HPFGUIDX 63716

Okay, having a debate on Harry's lineage.  In book 1 Hagrid says he's 
from a "wizarding family" which I take to mean James and Lily.  But 
later on in the books they mention that Harry is a half-blood.  So, 
my question is this:  Are Lily's family Muggles?  I really don't 
believe that James' family would have any Muggle blood in them due to 
the fact that he saw (conjecture here) his grandparents on his dad's 
side in the Mirror of Erised.  Can anyone clear this up for me?

Thanks!

Shelley