how to Rotate Camera around GameObject with mouse, where up is always up?

I made myself familiar with RotateAround() but I have an issue when using it together with my mouse to move a camera around another GameObject. When the Camera gets behind the object the controls for moving up and down switch around (kind of):

http://gfycat.com/AgileBigJellyfish

I don't wan't that movement to change. Also I want the camera to stop moving up/down if it's at the top or the bottom of the target GameObject.

My current script:

     public float speed;
     public GameObject target;
 
     void Update () {
 
         if (Input.GetMouseButton(0)) {
             transform.RotateAround(
                 target.transform.position,
                 target.transform.up,
                 Input.GetAxis("Mouse X") * speed);
             transform.RotateAround(
                 target.transform.position,
                 target.transform.right,
                 Input.GetAxis("Mouse Y") * speed);
         }
         transform.LookAt(target.transform, target.transform.up);
     }