From another blogger, I found this posting to be of interest and it might help you get your arms around how you define resilience to your staff and community partners. See Things to Make You Go Hmmm — About Community Resilience.
The item that resonated for me was the part on teamwork. Yes, you can be individually resilient, but if the community is going to be resilient it will take an effort by multiple parties to make that happen. And, the fact is that interdependencies do create vulnerabilities, but they can also add strength to a function if those connections are understood, valued and capitalized on.