There usually is some confusion as to what qualifies as a Pureblood or a Halfblood. It differs from site to site since really dear ol' J.K. was a bit vague. Below is what we at Ashes to Ashes will be using. Remember that most people are halfbloods if not less because of bloodlines.

COMMON
Squib + Squib = Muggle
Muggle + Muggle = Muggleborn
Muggle + Muggleborn = Muggleborn

Muggle + Halfblood = Halfblood
Muggleborn + Halfblood = Halfblood
Halfblood + Halfblood = Halfblood
Pureblood + Muggle = Halfblood
Pureblood + Muggleborn = Halfblood

Pureblood + Pureblood = Pureblood
Halfblood + Pureblood = Pureblood

RARE
Squib + Squib = Muggleborn
Muggle + Squib = Muggleborn
Muggleborn + Squib = Muggleborn
Halfblood + Squib = Halfblood
Pureblood + Squib = Halfblood
Pureblood + Pureblood = Squib