Health department regulations aren't going to permit an animal in food preparation areas. In this instance, those regulations do override the ADA (Americans with Disabilities Act) which applies to access in employment (it's Title I, as opposed to title III).
The ADA permits exceptions to access rights when the presence of the animal would fundamentally alter the goods or services being offered, which would be the case here. The ADA also permits an exception in the case of a direct threat to health and safety.
Under Title III, service dogs are permitted in the dining area, where the general public are permitted. They are not permitted in food preparation areas where the public are not permitted. Everyone behind the counter should be wearing protective clothing to contain their own body hair after all, and this would not adequately prevent contamination from the dog.
If your boss provides an area for the dog to be in that is away from food preparation, then maybe. But what is the point if the dog isn't going to be there to assist you he might as well stay home where he's more comfortable anyway.
U.S. Department of Justice's Toll-Free ADA Information Line:
800 - 514 - 0301 (voice)
800 - 514 - 0383 (TTY)
Edited to add:
There are several places were service dogs are not permitted. This article lists some of them:
http://www.servicedogcentral.org/content…
I'm a disability advocate specializing in service dog issues.