Assuming you get Residence, so will your husband. Anyone with Residence can work, not work, start a business, study - whatever they want.
I don't know where you got the idea from that link that people under the Family Stream (which your husband won't be, anyway) can't work - it only says that those
in a particular range of circumstances can't get a work visa.
If your partner holds a work visa for more than six months we may grant you a work visa for the same length of time your partner is allowed to work in New Zealand.
... However, you are not eligible for a work visa if your partner's work visa:
is a special visa that allows them to work in New Zealand until we verify their claim of refugee status
was granted under one of our working holiday schemes
was granted under the Pacific Quotas Residual Places Work Visa instructions
was granted under the Crew of foreign chartered fishing vessels instructions, or
was granted under the Recognised Seasonal Employer (RSE) Work instructions, or
was granted under the Skilled Migrant Category Job Search instructions.