Dishwasher and disposal receptacle
You cannot split a GFCI receptacle, however, a GFCI receptacle is not the only way to provide GFCI protection to a circuit.
GFCI Circuit Breaker
One option, would be to provide GFCI protection to the entire circuit by installing a GFCI circuit breaker.  Install a 20 ampere GFCI circuit breaker, and run 12 AWG copper conductors to the receptacle location.  Then you'll simply wire a standard receptacle, in a half switched configuration.
Blank Face GFCI Device
Another option, is to use a blank face (dead front) GFCI device to provide protection.

Install a double wide box at the receptacle location.
Connect the wires feeding into the box to the LINE terminals on the GFCI device.
Use the LOAD terminals on the device to feed a standard receptacle, wired in a half switched configuration.