To get an accurate readout of the above, look it up in a ChangeListener installed on engine.documentProperty().
I see http://javafx-jira.kenai.com/browse/RT-25004 "Allow for transparent backgrounds in WebView" has a related prerequisite case https://javafx-jira.kenai.com/browse/RT-29186, which is fixed for Java8.
In it's description is mentioned the following: "Furthermore, for those users who are comfortable using internal APIs, this will immediately make transparent background possible in WebView"
I'm trying to figure out what that internal API would be, but no luck so far. Tried following the links to the commits in the comments to get an idea, but they go nowhere (for me at least).
Anyone has an idea?