Interesting. I put some thought into how my setting's elves are different than human, but haven't given that much thought to half-elves. There was the one nation of half elves, where the elves, instead of dying off, had mixed with the humans that encroached on their lands in pre-history. They live in a slightly more urban elvish permaculture society guarding nature and the fey from other human nations as their kingdom is better suited to survive than the pure elvish people they replaced. Then I thought about royal linage with elvish blood for other human kingdoms with respects to stability of government. Great under a good king or queen, horrible under a seemingly immortal bad king or queen.
I think in the end, half elves either be oddities in either culture and resolved to be their own thing or group together to form some culture of their own.
I could totally see Drow creating an entire branch of Drow half elves to send as agents into the surface world. Most human cultures wouldn't care as long as there was money for them involved and the Drow are played up as merchants (in D3 at least). Then the half-elf Drow handler, who is also probably their ancestor, can play the "You're not like them; they'll never truely accept you as one of their own. I'm the only one you can really trust. We're family." for added loyalty.