As you are a newbie, I'd highly recommend using JavaFX 2.x rather than the soon to be unsupported JavaFX 1.x and JavaFX Script.
I'd also recommend posting any future questions to the JavaFX 2.x forum rather than the JavaFX 1.x forum.
JavaFX 2.x documentation is here:
For straight JFrames, the JavaFX equivalent is a Stage:
JavaFX doesn't have any functionality like that demonstrated in the Swing JInternalFrame Tutorial:
There is a request for a Docking Framework (which would presumably include similar functionality to JInternalFrame).
http://javafx-jira.kenai.com/browse/RT-14039 Docking Framework
It's currently tentatively scheduled for the major JavaFX release (8.0), but I'd bet that that particular feature will not be included in JavaFX 8.0 - there has been no recent discussion of it on the javafx mailing lists and such a significant feature would need to be started very early in the development cycle of the release (i.e. a month or two ago).
Your best bet if you want this kind of functionality at the moment is probably to use Swing (or something like NetBeans RCP) for your main app hosting the JInternalFrames and place JFXPanels in each of the JInternalFrames to make use of JavaFX.
If you are feeling ambitious, you could try to implement the feature yourself using the existing JavaFX classes.
I just voted for this http://javafx-jira.kenai.com/browse/RT-14039 Docking Framework. There seems to be substantial interest in this feature among the developer community. I wish it would endup in JavaFx8.
Native docking support will definitely take JavaFx to the next level and make it a compelling choice in the RIA space.