Yes they would be Halfblood because the blood status refers to wizarding ancestry.
If the Pureblood family was focused on blood purity, I would say they see it as "dirty" yes, i.e. Umbridge referring to them as "half breeds" like half giants, etc.
We would consider it too diluted probably but if it was something you were interested in I'm sure it could still be applied for and we can discuss in admin the limitations etc. I assume if anything they would just be "really, really, really, ridiculously good looking" (to quote zoolander).