With my Bebop 2 I can record video and also take a picture without interrupting the video. So far I haven't figured out how to do that with my P4. Is it possible? Every time I try now it stops the video.

While not a direct answer to your question I simply do a screen capture of the scene I want while I'm doing a playback of the video.  If you're shooting video at 1080p or better and have a large monitor (I'm using a 32' TV for mine) you can get an image that is just as good as doing a still photo.  I also tend to see more things on the video playback than I did while I was actually flying.

No ... not possible with the P4.
Stills or video but not both

Unfortunately it is not available in Phantom 4

Hopefully this will be coming in an update. It is very handy with my Parrot BB2.

I have the Bebop 2 and haven't figured out how to shoot video and take photos. I know how to, but at the end of the flight when it asks if I want to transfer the media, it only transfers the photo if I took a photo (and not the video). If I don't take a photo, it will transfer the video.