My husband and I recently got married. He lost his job. Can his ex-spouse come after my income for support.

You have no obligation to his ex-wife. However, if your husband falls behind on his support payments, the ex-wife can seek a violation in Family Court. If she is successful, she can obtain a money judgment which is a lien. This would allow her to collect on the judgment which means that anything you own with your husband may be subject to restraint such as bank accounts, vehicles, tax returns etc. Furthermore, your income will be relevant when it comes to a proceeding in court as to whether your husband can continue to make payments as originally ordered.  You personally will not have to pay but the fact that you earn a living may impact his case and in essence your money would in essence go to her.

No.  You have no legal obligation at all to his ex.  However, she can still go after your husband, and there will be problems if he doesn't pay her.

The news isn't all bad.  Your husband needs to talk to his divorce laywer -- or another one, if he would rather -- about getting his alimony stopped or reduced.  This would take a formal (written) motion or petition to the court, and it isn't simply a matter of proving that he lost his job.  He needs to start looking for a new job right away, of course, and he should keep very detailed records of his job search, because the court is likely to consider that in deciding the motion.

One place to find a divorce attorney, if he needs a new one, is our website, http://attorneypages.com