I found some helpful diagrams at do-it-yourself-help.com.
GFCI Protecting the Load
Wiring Ground Fault Circuit Interrupter Switch 
With this arrangement a
receptacle, switch and disposal are protected with the ground fault
breaker built into the device.
Not GFCI Protecting the Load
Wiring Ground Fault Interrupter and Light Switch 
With this
arrangement the receptacle is protected but the switch remains outside
the circuit. This arrangement can be used to control a light or other
device where the extra protection of a gfci is not necessary.
Ok I read your question a few times, so hope I understand what you want to do. You want GFI prtection on the outlet , but no GFI protection to the fridge. This will be easy to do if you can affirm that the load wire leaving the j-box where the switch and outlet are located, is actually the feed for the fridge. To check this out, you need to turn off the power, check the outlet at the sink and fridge to be sure they are ,in fact on same circuit and off. Now disconnect all the wires from the outlet and any wirenuts so everything is isolated. Now, carefully turn the power back on and check the hot (typically black) leads to ground with a volt meter to determine which one is the feed/source wire. Mark this with some red electrical tape. Double check to see that the fridge outlet is still dead.
Next, turn off the power and wire nut the black source wire and associated white neutral to the black and white wires you suspect goes to the fridge.( black to black, white to white) Turn the power back on and check with your voltmeter at fridge outlet again. If there is voltage there now, you have found the right feed wire to the fridge outlet. An alternate method of finding that wire with the power off, is to use an ohm meter. Assure the power is off, then twist the black and white together on the wire you suspect goes to fridge and check the hot and neutral slots of the fridge outlet with your ohm meter. the meter should show 0 ohms or "short circuit".
Now that you have identified the hot feed and load wire to fridge in your box, you can wire it so only the counter outlets are GFI protected. Put the source black wire together with the fridge black wire, along with a separate 8 inch piece of black wire (pig tail) and wire nut them all together. Use the 8 inch black wire to feed your switch/gfi hot. The neutrals tie together as usual with an extra pig tail for your GFI outlet neutral. Obviously, trim the pig tails to a comfortable length to fit in your box before connection to the GFI.
Since all outlets must be GFI protected in the counter outlet and since you cannot split a gfi outlet top and bottom like in your diagram, you have to do your light differently from your previous plan. I would suggest using a switch/single outlet device wired from the load side of the gfi. Wire the switch in series with this single outlet. This means only the single outlet is switched and gfi protected. You must have gfi protection on this outlet, as someone could unplug the lights and use it for something else.
Hopefully, one of my artistic buddies can do an edit and add a nice diagram depicting what I have outlined for you.
Best Answer
Install a 2-pole GFCI breaker in the panel
This is what's called a multi-wire branch circuit or MWBC. It is 2 sub-circuits fed off separate breakers. These 2 breakers are handle-tied because that is a safety requirement for MWBCs. That is also why neutral is pigtailed.
The split receptacle is a very typical use of an MWBC to deliver 2 sub-circuits to one recep. The switching is a neat trick.
The only way you can make this setup GFCI is to install a 2-pole GFCI breaker in the panel. Individual GFCI devices will not work because there isn't space for them.
Note that your current breakers are half-width (we call 'em "double-stuff") and that means you will need to find some more space in your panel. There's no such thing as a half-width GFCI breaker.
However, if you are able to run new cable between the switch and receptacle, and are able to blow out the under-sink receptacle into a 2-gang, then you could fit a GFCI+switch device in the current switch location, and a plain recep and GFCI downstairs. use either 2 cables or /2/2 cable; mark one of the cables' wires purple and gray (gray=neutral), and the other hot wire red.
The key to it is the separate neutrals past the first GFCI. That's why you can't do it with cables as-installed except by using a 2-pole GFCI breaker.