I worked in a county public health department for about 5 or 6 years. We were large enough to be departmentalized but small enough that many of us worked more than one program, so fingers in many pies. I think they were looking for broad based experience, an ability to do independent and critical thinking, acceptance of a broad base of lifestyles. Depending on your region, fluency in a second language can be a boon. I think experience with children and families can be helpful, though I really didn't have any and I learned a lot about children and families working at the HD. Nurses who "didn't make it" at our health department were sometimes stymied by the lifestyles issues. Working with people who present for HIV counseling and testing, STD treatment, teens in pregnancy prevention/birth control and high risk, often teen parenting, can present ethical dilemma that some people cannot resolve or live with. Again, depending on what program you are looking at, there is a lot of working by protocol, but you have to exercise alot of judgement on when to implement the protocol (vaccines, STD's, HIV testing, blood pressure screening all are protocol based).
You will undoubtedly see your community and your county in a whole new light if you take the job and work for your community in this fashion.
I also enjoyed being connected to an information system that included the state department of health and, ultimately, the CDC.
Good luck in your interview.