How do I deal with a jerky brother-in-law?

So my brother-in-law thinks he's the greatest thing since sliced bread, and is a complete jerk to me. Every time I do something for someone in his family, he accuses me of "stealing them away" or trying to "compete". Neither accusation is at all true. He just has lots of issues. The latest was a huge fight at Thanksgiving where he got angry at me for making dinner. Tomorrow is my Father-in-law's birthday, and we're going out to dinner. It's just going to be the 5 of us. I don't think the silent treatment is okay, but I really have nothing to say to him, and I know it's going to be awkward. I also want him to know that the way he treats me isn't right, so I don't want to just sweep it under the rug. At the same time though, I don't want my FIL's b-day dinner to be ruined by all the tension. What would be an appropriate way to handle this situation?