M.M.
Have you and your husband discussed what the rules for your daughter need to be? I think a lot can be solved by coming to an agreement on the rules and then sticking with them 100%. Then you and he can confidently stay on the same side, letting your daughter know that she can't play both sides just so she can get what she wants.
I've been in the same situation. My husband is my daughter's step father and they do get into arguments at times that have nothing to do with anything. Sometimes I've just yelled and demanded that they both stop immediately. We camp and the close quarters we're in when it's crummy out has lead to what I just described.
Most often I find it best to juts walk away and let them duke it out. Arguing can be healthy and some people just enjoy it. My dad and I argued all of the time - we were at opposite ends of the political aisle from the time I was 5. It drove my mom nuts, but he and I enjoyed our arguments even when they became a bit tense. As a result, I feel comfortable standing up for what I believe. I feel comfortable disagreeing with my friends, my husband, my family and being my own person.
So long as no one is storming out of the room, your daughter is getting to see that she can push a bit and argue a bit and that no one is going to walk away from her because of it.