"She is so cute, I just want to bite her face."
"Oh, bite his face, he's such a cute stinker."
"Bite your face -- aren't you a doll!"
All these phrases -- plus several other permutations referring to babies, toddlers, and/or considerate young men who are being unintentionally romantic -- are correct uses of the expression "to bite one's face."
Though it sounds cannibalistic, biting one's face is a term of endearment, meant to signify only the highest level of charm and cuteness. It is a distant cousin of the accepted idiom "eat it up" (particularly when applied to children, as in "you're so cute, I could eat you up.")
The phrase originated about 10 years ago among the IMS-stricken community, and has since spread to this group's closest friends and family. It is now common practice to exchange emails and phone messages centered solely on exclamations of "bite his/her face!"
Do not be alarmed if you hear this phrase issue from the lips of a person you've known to be sane, balanced, and safe to allow near children up to that point. They mean no harm; they simply can't contain their overwhelming urge to squeeze, snuggle, and kiss whatever/whoever it is that warranted the outburst in the first place.
Note: It's best not to stand in their way. Simply step aside, and let them carry on. Everyone will be happier for it.
* As in, if you don't want to bite their faces, you have no soul.