Half-Elves move a lot more freely in Human society than do pure-blood Elves, mainly because it's easier for them to pass for Human.
If they are revealed as having part elvish ancestry, they're very likely to be shunned and discriminated against — the days of Elvish domination may be far in the past, but their reputation lives on on tales of Ancient Times, when Elvish overlords exercised ruthless powers of life or death over whole populations, and humanity was utterly subservient to their will. There are plenty of superstitions about the Elves, few of them complimentary, and though the learned may know them for the fictions they (mostly) are (these days), most of the ruck and swill of humanity still give them full credence.
The situation in Elvish society is different, but certainly no easier for the half-Elf. Even fairly tolerant, enlightened Elves tend to view Humans with a degree of distaste — to the Elves, humanity (and pretty much all the non-fey humanoids) are untermensch; at best, barbaric, and at worst, actually bestial. Half-elves are therefore, at best, objects of pity, being as they are the products of bestiality. In the more xenophobic Elvish domains, a half-Elf is an abomination to be expunged as quickly as possible.
Probably the most congenial societies for the half-Elf to live among, as far as acceptance goes, are those small, primitive tribes of Wild Elves, who have fallen far away from the knowledge and mores of old, and to whom purity of blood is much less important than the individual's usefulness to the tribe. Life among the Wild Elves is far from easy though; they live fearful, furtive lives of hiding, hunting, and being hunted in turn.