Well, in the Marine Corps it is required to get a waiver if the enlistee has even one dependent and generally speaking the military does not allow people to enlist with more than two dependents. That is not to say people don't get waivers for having more than two dependents.
My father in law was in the Corps and enlisted with THREE dependents, his wife and two children.
VANCAM1: Tell your husband to tell the recruiter to request a waiver. There's no guarantee it will get approved, but it's worth a try, right?