This is not about driving the vehicle, it is about improper display. Talk with an Anchorage attorney about what kind of fees you're looking at and where to get your plates.
This answer is given merely for informational purposes and does not create an attorney-client relationship. For specific advice, contact an attorney in your state to see if working together makes sense.
It's most likely that the police seized your plates as evidence of the crime your boyfriend is charged with. If that's the case, you will have to wait until about 30 days after his case is over to get your plates back from the police department. There isn't any way to make them turn over their evidence from a pending case.
You can request a new set of plates from the DMV if you need plates now. That may involve a fee.