Hi Hilary,
The problem with allergies/asthma is that many times its related to a specific individual. There's no solid rule for how everyone relates to any particular breed or even individual dogs.
Personally, I believe that Airedales with their wirey and non-shedding coats should be a good canidate. But that person should visit as many examples of the breed and their homes to determine if there is a problem that they can. Even then, bringing home a puppy, waiting until it's adult coat can also trigger problems.... or none. It's just hard to tell. :)
Airedales are lovely dogs, but they are the largest terrier breed with all of the independent instinct imbued in the terrier grouping. It does take a bit of patience and training to raise one. It's one of those breeds that are usually not advised for a first-time dog owner.
If you have further questions about the breed, look into the Airedale breed club ---either in UK, USA, or Canada. Since I don't know your location, I can't provide links. Just do a search on google. The sites have FAQs and you'll be able to talk with individuals who specialize in the breed.
hth and good luck,
toodles