My husband and I are getting divorced and currently living as roommates. He's on the lease but has never paid any rent or utilities the whole time we have lived here. I want him to move out, but he refuses. What can I do to make him leave?

You have to follow the eviction laws in your state but I doubt this will work prior to your final divorce. This issue needs to be addressed in the final decree. Right now you are not really his LL so the eviction will not work, your are co-tenants with equal rights.

File a motion requiring him to establish a separate residence.

This isn't a real estate issue but a divorce issue. He is on the lease so you can't evict him. You have to get the divorce court to force him out.