What size is your yard, how old are your kids and how many chickens do you have?
There are a couple illnesses that can be transmitted to humans from birds, but it's not that easy if you aren't the one cleaning their coop, butchering them, etc.
Chickens are a fabulous way for children to learn to care for an animal and to learn where food comes from without getting into the butchering business right off the bat. I have an 8 year old daughter and she LOVES the chickens and ducks. We recently took several of our birds to the high school for the FFA kids to see and I couldn't believe how much information my little girl was able to share with all those teenagers about raising poultry!
You wife might have grown up, as I did, thinking chickens are dirty. That's all I heard from my parents when I was growing up. They really aren't though. I think it just seems that way because they poop indescriminately. We have a 10x10 coop with a 2x5 "bedroom" for the chickens and the bedding needs changed anywhere from once a week to once every 3 weeks. We have ducks too and they are much, much messier! We also free range our birds on what's left of our 1/2 acre after you take away for the footprint of the house, garage and shop. We don't have grass, just rock and wild plants, and I really don't notice the chicken poop being an issue. Granted, we get a lot of rain that washes it away, but still.
If you have bug problems the chickens will take care of that in a hurry. If you have a garden area or your wife has flowering bushes, you may want to put some chicken wire around those. But other than that I wouldn't say they have made our yard any "dirtier". Just teach the kids to use antibacterial rub after petting the chickens and they will be fine.
You'll love having the birds and many a dissenting spouse has later been found to be the most doting "chicken parent" there is.
ETA - Holy typing errors!