He's supposed to get the anthrax vaccine multiple times. It's a five dose series, so unless you mean he's gotten the five dose series three times, which would be fifteen shots, then there's nothing out of the ordinary with him having gotten three anthrax shots. However, he should go in and report it if he's having a reaction. Serious reactions to the anthrax vaccine usually don't happen until someone has had multiple doses and they know this, so he really should report it. Does he have any swelling? If he has serious pain and swelling, that would be a contraindication for further doses.
My DH did fine with the first three or four doses, but the last one he got (I can't remember if it was the fourth or fifth) caused him a lot of problems. We don't vax DD or myself either, so I know how you feel.