If a Pure-Blood was to have a child with a Muggleborn/Muggle/Half-Blood, a Half-Blood offspring would happen. (That or a Squib, a child of two or one magical parent, but doesn't/limited magical abilities)
If a Half-Blood were to mate with a Muggle-born/Muggle/Half-Blood, the child would be a Half-Blood (Or a Squib)
If a Muggle-Born and a Muggle were to mate the child would be a Half-Blood
Muggle-Borns doesn't mean you were born from all Muggles and somehow you ended up with Magical blood. Some point, whether a million years back or sixty years, a Squib was born from a Magical family. The Squib would in turn pass the magical gene down and somehow the Muggle-Born ended up with a stronger magical genetic, thus making the child a full wizard/witch.
The term "Half-Blood" means you have both Magical and Muggle blood in you. Regardless if it was four generations prior to your birth, Muggle-Blood still lingers as well as Magical. To be considered a "Muggle-Born" both of your parents have to be Muggles. But technically, you're a Half-Blood. Just like Squibs are technically a Half-Blood/Pureblood.
Just to be more detailed, to be considered a Pureblood, you have to come from at least seven generations of wizards/witches (Not Squibs) on both sides. JK Rowling had said there isn't a Pureblood family left, as all families have had at least one Squib/Muggle-Born parent at some point. The Pure-Blood families considered themselves Purebloods simply because they're the offspring of seven generations of magic.
Everyone is Half-Blood is the easiest way to explain it! :)
See...
Muggleborn + pureblood = Half-Blood
Muggleborn+Muggleborn= Half-Blood
Halfblood+ Pureblood= Half-Blood
Halfblood + Halfblood= Half-Blood
Muggleborn+ Halfblood= Half-Blood
Muggle+ Halfblood= Half-Blood
Muggle+ Muggleborn= Half-Blood
The only time a child is considered a Pureblood if both parents are Purebloods. A Muggle-Born if both parents are Muggles. A Half-Blood for none of the above!