, they probably want to see both if the addresses are different. The Blue Book is the basis for making an invitation to an alien but if the alien is invited to stay somewhere different, then you will need both - plus copy of owners ID card.
, the Blue Book, and the Deed are different. You can only stay at one place but your name should be on the Deep for all properties. In this case they are probably asking for both the Blue Book of the owner and the Deep of the property where the OP is staying.