My company employs several department heads who regularly speak negatively of employees in other departments on subjects that are only remotely related to their jurisdictions. As a mid-level manager, how can I defend myself and request that they back-off, while respecting the level of influence they have on my future and the organization?
This can be quite difficult to address, as you correctly point out. It is important to address because productivity is adversely affected by this type of behavior.
First, the behavior indicates a lack of a clear shared goal between departments.
You can help resolve this at your level by continuing to ask in a supportive tone: I understand our department’s goal, and I understand what department xxx is attempting to do, what I don't see is how our goal and their goal is part of the same bigger goal. What's the common goal we all share?
We’ve seen instances where asking this question upwardly (up the chain of command) continues to bump up the chain rather rapidly and creates dialogue about the shared goal at the senior management level.
Secondly, ask about their specific concern and what would address the concern. For example “I hear you are upset about some things that are going on. What specifically is your concern, and what is one way to address that concern?” By acknowledging their concerns and validating their thought process, you demonstrate consideration and cooperation. Also, by requesting that they offer solutions to address the concern, you remind them that there are proactive steps they can take and requests they can make (vs. simply complaining / blaming). As you listen, remember to grab the facts and let the emotion flow past you so that you don’t get caught up in emotional reactivity yourself. Encourage them to make the request to the right person….as in “That seems like a reasonable request, perhaps you can put that on the table with xyz person."
Finally, hold a boundary around badmouthing, as in, “We all get annoyed at times…I’d like us to agree to handle that annoyance by making specific requests to those involved rather than to complaining in ways that lower morale. I promise to say the same thing to anyone who complains about you to me!”