I would like to know if it is possible to program the Arduino Ethernet board with an Arduino UNO SMD Edition
Yes, it can be done. How you do it depends on what you mean by "program the Arduino Ethernet board" and "with an Arduino UNO SMD Edition".
If you mean "upload sketches" and "using the UNO SMD as a dumb USB-to-Serial converter" then you just wire the Reset pin to a Ground pin to disable the processor on the UNO SMD. Then use Pin 0 and Pin 1 for your serial connections. You'll also need Ground and you will have to do a manual reset on the Arduino Ethernet to begin the upload.