Elementalist
The short answer is "it depends".
The less short answer is "it depends on whether they're the sort of people who are capable of ignoring how they feel about each other if there is a need for it, and on how they actually define that need, and it is quite unlikely to work due to scarcity of people of the sort you need though not entirely unheard of".
And the long answer is this:
Yes, it is possible. But whether it would work is up to how you write it. People can hate each other for a plethora of reasons, not all of them what we'd call "rational" ones, and depending on what the reason is exactly and on what sort of people those characters are, it is potentially (but not assuredly) possible for them to work together when it is necessary without even undermining the other one but hate each other with passion.
So really, you have to start with the characters and with the reasons for the sort of relationship they have. Once you get there you'll see if it's actually possible for them to work with each other despite their feelings.
Beware, however, of trying to shoehorn it in when it doesn't fit, and of changing "one or two things about the characters" to make it appear that they can work with each other when it doesn't really feel as if they would. For all the traits that would make it possible for that to work are major enough that for most authors (and sorry if I sound harsh but you most likely are not one of the minority who are the exceptions) changing that means rewriting the characters from scratch and most likely without the "hate" part.
One thing that may help you is the fact that both sense of duty and nobility are such traits; characters who are written around those concepts from the very beginning are more likely than not the sort of people who would just grit their teeth and work together with someone they hate because there is a need for it.
What they argue about is pretty important to them personally, enough for there to be a big deal when they both agree, and so...let there often be a bigger deal to test their pettiness. (I'm thinking Simon Tam and Jayne against the Reavers in Firefly. Slobs Versus Snobs goes out the window when you're locked in a room with a Complete Monster hammering on the outside trying to get in.)
Alternatively, they could argue plans that are on equal merits but not take barbs personally. Or, have only one take it personally and keep that personal wound personal, and never be pushed to villainy but just stew in annoyance.\\Edit to add: Discard this paragraph, that's more of a rivalry, and you said it wasn't a rivalry but deep hatred.
edited 4th Jul '15 10:53:54 PM by Faemonic
So I'm working on writing a group where two characters-the Hero and Lancer-hate each other. I don't mean a rivalry or a constant taunting, I mean hating each other with a passion. They get along genuinely well with the other characters-for the most part. It's just these two who hate each other enough to fight each other if left in the same room alone.
So, would this kind of relationship work if these characters are suppose to be working together?