Hopefully this reading order is going to be easier and far-less convoluted than No Man's Land.
Here we go - ordering by release date:
Gotham Gazette: Batman Dead? - 3/04/2009
Batman: Battle for the Cowl #1 - 3/11/2009
Azrael: Death's Dark Knight #1 - 3/18/2009
Battle for the Cowl: Commissioner Gordon - 3/25/2009
Oracle: The Cure #1 - 3/25/2009
Batman: Battle for the Cowl #2 - 4/08/2009
Battle for the Cowl: Man-Bat - 4/1/2009
Oracle: The Cure #2 - 4/15/2009
Azrael: Death's Dark Knight #2 - 4/22/2009
Battle for the Cowl: Arkham Asylum - 4/22/2009
Battle for the Cowl: The Underground - 4/29/2009
Battle for the Cowl: The Network - 5/06/2009
Azrael: Death's Dark Knight #3 - 5/13/2009
Oracle: The Cure #3 - 5/13/2009
Secret Six #9 - 5/13/2009
Batman: Battle for the Cowl #3 - 5/20/2009
Gotham Gazette: Batman Alive? - 5/28/2009
I didn't actually grab the Azrael issues yet so I can't really speak to the entire order, but mostly this seems to be the ideal way to read through them. Mostly it seems that publishers haven't gotten better at releasing things in the order in which they should be read, but there have been a few mistakes from time to time.
If anyone has any additions or corrections to this list, please let me know.