How to handle a supervisor?

report it to HR, this sounds like an illegal action

That sounds like a military problem.

What can he do at this point basically?

Either file a grievance to HR or look for a new job..

will"his boss" stand up for him"?

What kind of an answer are you looking for here?  The hotline for the Politeness Police to call them in to make these people be nice to your husband?  The options are pretty simple:

Work harder at whatever these people are wanting him to do to try to please them.

Talk to his boss to find out what he's doing wrong so he can improve.

Keep doing what he's doing and not care what people he doesn't report to says or does.

Be a baby and throw tantrums.

Leave.

Now as for these 'certifications' you like to refer to.  If it is a professional certification, they belong to him not the company.  The company cannot take them away.  If it is an internal thing that the company does, it will have no value outside the company.  So it doesn't matter what they do with them.

Demons and artists cooperate for you common goal, Ignorance!

My husband has talked to his supervisor, the problem supervisor as well as higher up. He is a contractor. So, his HR people are different than the HR people of the problem supervisor’s. (My husbands HR office is located out of state). He also does have another job lined up. Yet, it won’t start for another 2 months. His certifications he earned through the company while working for them. Can the supervisor really not take his certifications away? 

Get a new Job, then Quit on the spot.

OR

Write down Names, Places, Dates, Times, and Problem, then hand it to Human Resources.

Best to have a new job in advance.

Your husband isn't telling you the truth.

The certificates your husband earned cannot be taken away.  He earned them like a college degree.

Can your husband be demoted and not use the certifications on the job?  Sure. 

What should your husband do?  Talk with his immediate supervisor and manager. 

This is a conversation he should have with his direct supervisor.  The question he needs to ask is "What do I need to do to be successful?"  Those exact words.  His supervisor should say specifically what he expects.  If he is allusive or non-specific, your husband should then give a couple of examples of what's going on, then repeat the question of what he needs to do to be successful.  This forces the supervisor to step up and either intervene on your husband's behalf or give guidance as to what your husband can do differently to succeed.