Yes, both you and your U.S. citizen spouse will be interviewed before you get your Green Card if you applied for Adjustment of Status. In the case of Consular Processing your U.S. citizen spouse is not required to attend the interview.
Note: The purpose of the interview is to determine that the marriage was entered into in good faith and that all USCIS Forms have been correctly completed.
The processing time for a Work Permit varies depending on the work load of the Service Center where your petition has been filed. The process usually takes 60 to 120 days after the petition is filed.