My husband is a green card holder, would he be able to sponsor his niece (she has a husband and a baby) or is it just limited to parents, brothers, sisters? thanks!

For either US Citizens or Greencard holders sponsoring someone for a greencard you are limited to "Immediate" family members only. Parents, children, sisters/brothers.

The niece would have to have an immediate family member here in the states that could sponsor her and her family.