All credit for this goes to Pasqu0 on the EA UK Forums and this post.

Since so many of us use Steam, having to shift over to Origin's community system has been a minor irritant at least, and a crime against PC gaming at the worst, depending on your personal opinion. Well fear not fellow Steam users, because here is a valid workaround! This will allow you to run the steam overlay in Battlefield 3 and Origin's overlay at the same time.

1. Go to your Steam Library and select "add a non-steam game."
2. From there browse to your Origin folder (C\Program Files (x86)\Origin\) and add Origin.exe to your steam games list.
3. From now on launch Origin from your steam games library or from a shortcut created by steam

Note: Steam will automatically display that you are in a non steam game called Origin on your friends list. If you'd like, you can right click Origin in your Steam Library and select properties. In the following menu you can rename Origin to "Battlefield 3 Limited Edition" or whatever you'd prefer.

4. You should now be able to use the Steam Overlay and the Origin Overlay while in any Origin Game. Make sure that you set the overlay key binding for Origin to something different from Steam's though.