No, you cannot do that natively on the iPhone, once you start to record through one camera you need to stop the recording to change the camera being used, and there is no picture in picture option in the native Camera App.
There are, however, Camera Apps in the store that will let you do this.
http://www.iphonehacks.com/2015/05/how-to-record-reaction-videos-with-front-and- rear-camera.html
However generally videos like the ones you describe ae done in post-production and editing, by adding a secondary video to the primary one in editing.