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How many 'babies' are we talking about here?  I can see trying to argue that 2 or 3 chickens are household pets, but I would bet you'd have a hard time arguing the same principle with a flock of 15 or 20.
However, if you have vet records on the birds, it would show that they are more than just farm-type animals.  ( most production flocks, whether meat, egg, or both don't get that treatment.) 
If you sell eggs or raise meat birds (either to sale or for yourself) then the birds will likely not be considered pets, even if you have a 'chosen few' that would never go into the stewpot.  Similarly, if you hatch, advertise, and sell birds, they would likely not be considered pets- even though people sell 'normal' pet animals all the time...
Also, if you can show that the birds have had a cocci and marek's vaccine from the hatchery (assuming you purchased from one), would help to deter the 'chickens are dirty and diseased' angle.  As would any other flock health certifications you may have gotten.
What are their housing conditions?  If you can describe a routine cleaning and maintenance schedule you follow regarding the flocks housing, it should help, again to avoid the above arguements. 
Do you routinely add or detract from the flock?  Being able to show that you've owned the same birds for a number of years definitely should help to show they are pets.
Can you approach the chickens without them acting fearful?  Can you pick them up and hold them without a struggle?
What exactly is the reason the city wants to remove your animals?  How did they find out you have them?  Crowing rooster?  Stinky coop?  Are they annoying the neighbors?
Don't get me wrong, I'm just playing devil's advocate, trying to think of some reasons to suggest that your birds are NOT pets- so that you will have good rebuttals if needed.