Multitasking on iPhone 5s while HDMI displays something else? How can I keep HDMI playing movies while using other apps on my handset?

I initially thought that the adapter merely mirrored pixel-for-pixel, but during movie playback it is possible to reveal the double-tap application menu without affecting playback; selecting an app results on its being displayed on both displays and halting movie playback.

iOS 7.1.2, Apple Lightning-to-HDMI adapter, HDTV, Netflix app.

I would prefer a factory setting or approved app to achieve this, but please do include jb solution if applicable.
Lock the phone, swipe to the left then back. Swipe up to bring up the calculator and then unlock the screen.
You should now be able to multitask.