Rotation along two axes only?

Hello. I am developing a space shooter similar to this. In that game, the player's ship will follow the crosshairs, but will not rotate along the z axis (it will not "do a barrel roll"...couldn't resist). How is it able to do that?

In my prototype I have been working on, I have a look at function thats attatched to the ship (where the look at target is the crosshair object, which is just an object that uses a drag script to follow the mouse around the screen). But, the ship will rotate around the z axis(technically its the y axis, because to use the drag object script, the crosshairs had to be positioned as if the player was looking at everything from above).

Thanks

Here is my prototype

http://forum.unity3d.com/threads/86174-Rotating-object-on-2-axis