For years (seriously), the Hulu website has had this to day:
Q : I use dual monitors but can't run full screen on one and work in the other screen at the same time. How come?
This is currently a limitation with the Flash Player which we're using to stream our content. As a short-term workaround, you can maximize the pop out player instead. This will achieve nearly the same effect and allow you to work on the other monitor.
We're continuing to investigate possible solutions as we want to take good care of our multi-tasking users.I don’t really believe they’re investigating squat. Again, it’s been years.
If you use the above workaround, you’ll have addresses and folders and such at the top and bottom of your screen. You could also use the dedicated Hulu desktop player.
I just wish they’d fix the problem.