Run Steam as Administrator (right-click on the Steam icon and click on "Run As Administrator").
Install Arma 2.
Run Arma 2 once.
Install Operation Arrowhead.
Run Operation Arrowhead through Steam (Battleye will now install automatically).
If you wish, you can also install the Arma 2: Operation Arrowhead beta (for the purposes of running Mods etc.). It will appear as a separate item in your Library.