Legal Question in Immigration Law in Massachusetts

You cannot work without explicit, approved, valid work authorization from USCIS (such as an approved I-765 (EAD), OPT, H-1B, etc).

When you state your "husband's company has applied for greencard", does that mean you & your husband filed your I-485 applications, pursuant to an approved labor cert & I-140, with a current priority date?

If so, then you would have filed form I-765 for a work permit (EAD). Once you get the work permit application approved, you can work for anyone, anywhere in the U.S.

I recommend that your husband discuss his case, in detail, with the employer's attorney & get a copy of the pertinent forms, approval & receipt notices, as they apply to his case.