Create a Communication Sniffer
Use two serial port adaptor RX channels (ftdi usb adaptors), one for each direction. Realterm has a Monitor mode where it will take the RX from two different ports and interleave it on screen in different colors. You will want a recent version. If you have an old school 2/4port serial adaptor (not usb) it will work better in terms of not messing up the timing between the two channels. If it is all fairly slow, no problems. Realterm can also put timestamps into the data if useful.
Use an oscilloscope or logic analyser. Some can decode the data for you
use a single serial port and OR the two directions together. Only works if they don't talk at the same time, and you can make some sense of what is going back and forth.
Make a special adaptor from a micro with two uarts. Send each byte of the incoming data out as two bytes, using a bit to identify which rx it came from. [you can have 1 bit for channel, 1 for B7 of data,6 for a timestamp, or monitor a couple of pins]. Using ftdi usb adaptor, you can output at 3MB, which would allow 150kBd on the rx channels (in total). This method would also make it possible to handle 9 bit protocols too.  Arduino Mega would be perfect for this as it has 4 uarts and usb already on board