That links says that the devices provide serial communication capabilities. That means that either device can talk at any time, and the other device is free to listen or talk at any time.
You will need to establish some sort of protocol. Basically, one device is the master. The other is a slave. The slave doesn't speak until spoken to, at which time it must reply immediately.
One thing that the master could do is periodically ask the slave if it has anything to say. If the slave says that it does, the master can ask it what is has to say, and react accordingly, effectively reversing the "master"/"slave" relationship.
The master could also ask the question "Do you need to be master now?", and, if the slave says yes, the master becomes the slave, and the slave becomes the master.