Have you got the spaces toolbar open? (That is the arrow thingy on the very left of the status bar at the bottom of Thunderbird.) The address book is the second item in the icon list. As far as I can figure it, the spaces items are available from any tab in the mail application window.
Or you could use the shortcut Alt+2 that opens the address book
Or you could customise the toolbar on the top of the window to show the address book icon. Not as universally available as the spaces toolbar, but my choice.