While not all that common, I have seen this before. It's done this way so that you can pull the full 15A from both the top and bottom section simultaneously without tripping the breaker. Say you have a microwave oven and a toaster, or a toaster and a waffle iron, etc that you want to use at the same time. In my kitchen I have to be careful to coordinate use or I trip the breaker.
You won't be able to split GFCIs like this, so a couple of options I can think of:
- Install a dual-gang box in the first of the run and put two GFCI receptacles in there, one on each circuit.
- Install a GFCI on the first receptacle, and wire nut the other circuit together as a passthrough, then install a GFCI receptacle on that circuit in the next box over, passing the first one through. That will require some investigation to determine where the run starts in order to ensure that all kitchen receptacles are downstream of the GFCIs.
- Leave the receptacles alone and replace the breakers that feed them with GFCI breakers in the panel. This is what I would personally be inclined to do, I hate hunting for reset buttons on individual receptacles and prefer to have everything centralized.
As with anything of this nature, refer to your local electrical codes over any advice given in a forum including mine. Talk to an inspector if necessary or hire a licensed electrician if you have any doubts about doing the job yourself.
Edit: I see you've updated your original post since I replied. The diagram you show is the usual way of wiring GFCI receptacles, except that in your case it sounds like you have two runs sharing the same boxes, which will require two GFCIs.