On tactic that finally worked for me was to involve them in a relatively non-destructive way and let them just begin to learn what all is involved and the responsibilities therein. This process helped build relationships and respect for what all was involved. At the same time, show interest in what their challenges are, and solutions. They learn, you learn and so on.
This is what I am going to aim for, but I'm afraid this is going to end in a battle that ends with total control for one of the two departements.
Probably IT :-( When it comes to convincing the man upstairs it is hard to beat a zillion pages of ITIL based theory...