Shard is right. Although I agree -- I don't know why. It's only physical armor that stacks with shield, not an armor bonus.
Here's a question, my 5th level Wizard got himself a HUGE armor class last game ... He's got a high dex (+4 dex bonus) and cast haste (+4 haste bonus) then shield (+7 reflex bonus) and already had mage armor up since it lasts for hours (+4 armor bonus).
In one round, he'd stacked himself with a 29 AC which made him unhitable to most of the Orc tribe we were facing. Now I realize, one dispel magic and he's down, but a 29 AC at 5th level is pretty tough (the DM thought so). Did we do anything wrong?