It's not possible to access Battle.net with the same CDKey, if you both want to play together. If one of you plays on USEast and the other plays on USWest, then it'll work, but you can't play together.
If multiple players wish to play the game at the same time, each player will need their own copy of the game. If an expansion is being played, each user will need their own copy of the original game and the expansion. Multiple users may not share the original game.
According to the End User License Agreement, the following applies:
"...by installing the Program you thereby accept, a limited, non-exclusive license and right to install and use one (1) copy of the Program for your use on either a home, business, or portable computer."