Don't stop with the separate debriefing--it's equally important to look at the exercise together. Part of what make it possible for members of different agencies to work together seamlessly is understanding each other's point of view. You won't get that perspective unless you also review the training jointly. You may be surprised by what you learn when you see your own actions through the eyes of others. You may even find that looking at the training together will generate creative solutions to long-standing areas of friction.
Joint training exercises have another benefit as well. Next time you work with a firefighter or paramedic at an emergency scene or provide protection for a parole agent conducting an unannounced search of a client's residence, you'll have a link through common experience, making things go a little smoother. Who knows? It might work so well you expand the idea of joint training to civilian agencies such as Child Protective Services or the local Mental Health Crisis Team. Joint training--especially scenario-based training--takes effort to put together, but it can result in less frustration for the cop on the job and better service for our communities.