Do you know who is the head of the subsidiary reports to? Your hu*****and can talk to this person first. I assume it's someone from the parent company? It this won’t work out, then your hu*****and can report this to the HR of the parent company. The key depends on 2 things:
1. Whether the parent company is a big company. The bigger the company, the better, because no big company wants to involve in a lawsuit of his own employee. If it is a big company, they HR can prove what you said it’s true. The most likely outcome is they will fire your hu*****and’s direct manager maybe also the head of the subsidiary. It’s also possible that they will transfer your hu*****and to some other department to the parent company.
2. Second, you have to report this to HR whether the subsidiary HR or the parent company HR. If no reporting, you have no case. You need to file a complaint to HR for a record at least.
I don’t think it’s wise to resign first and file a complaint. You have to be the employee of the company to complaint. Otherwise, why should they care? When you talk to HR, you need to state the facts, be professional, and try to gather some evidence.
What your hu*****and’s manager asked him to do is definitely wrong; you have to fight against it. Good luck!