If you don't stop the serial port or the PC between bytes, you can't send several bytes from the PC to de uP. You know that you PC is faster than you uP. You must use de signal DTR of the COM port of the PC. You must connect this signal to a port of you uP. Then, when the serial interrupt start in your uP, you must set this signal to stop the PC. When you finish of proccesing the byte, you can unset this signal.