How can I make my GameObject rotate this way?

Hey there! I am in the process of creating a space game and have found a temporary solution for the rotation of the player ship, however I am looking to make it rotate like the ship does in this video: https://www.youtube.com/watch?v=xQ2KFd7811U (see at 42 seconds). As of right now, I am using Quaternion.Lerp to move the ship's angles to where the camera faces. The camera is setup in a third person style and the mouse moves the camera in any direction. The general idea is that the player ship will point in the direction that I have the mouse/camera, however I am looking for a method to make the ship move like that of what is seen in the video.

My current setup only allows for the ship to rotate along the X and Y axis. It never uses the Z axis to turn like the ship does in the video. Thanks for your help! If you need to see any code, just let me know.