Interrupts and Arduino EthernetShield
Interrupts on the ethernet shield are not supported by stock library. (don't think anyone has gotten it to work). Noting the RF Link is a receiver and will be connected to the RX of the Serial. The Arduino's Serial Library will collected this using interrupts (per byte) into the Serial Buffer, to be read by your application. So as long as the Serial Data does not exceed the rx buffer between reads, your main loop simply need to service both objects... inByte = Serial.read(); building your string, then when you so desire send client.print what you want to your destination. Neither of these read or prints are blocking.

Look at the example ..\libraries\Ethernet\examples\TelnetClient\TelnetClient.ino

Where you can add framing of the serial listened data and then putting the desired results to a wput. as done in example ..\libraries\Ethernet\examples\PachubeClientString\PachubeClientString.ino