Since your husband is a Swedish citizen, he shouldn't have an issue finding work. Have a look at the Swedish jobseeker's website. How fast it happens will depend on many circumstances, however. What does he do?
You can read our guide on visas for Sweden for a quick overview, but your best bet is to use the official migration website.
Hope this helps!
Did you have any luck with the advice provided? I am thinking of moving to Stockholm with my two girls and wife, but I have not been able to land a job. Any useful tips that you learned from you last post?