Just got re-married with 2 young kids. How do you handle christmas and the ex husband. He wants to be there?

Ex-husband want to spend christmas eve and christmas morning with me, my children (11 and 6), and my new husband. We are trying to get along for the kids and make the best of a difficult situation. Our divorce could have been a whole lot worse and we have tried to remain friends. My new husbad is uncomfortable but will accept my wishes. Any input would be appreciated.