While most Linux applications work well with docking, such as Pidgin or Lottanzb, this is cannot be done for Firefox and Thunderbird. However, it can be very handy to have the two programs docked separately in the indicator panel. On the add-on site of Mozilla a very useful add-on is available: Fire Tray.
Fire Tray is an add-on that works with Firefox, Thunderbird, Sunbird, Seamonkey and Songbird. The advantages of Fire Tray includes displaying unread e-mail of Thunderbird or playing multimedia in Songbird using the media keys on the keyboard. The applications remain running in the background without being displayed maximized on the desktop.
The Fire Tray add-on can be found here.