Only one person can be listed as the transferee if you use a ATF 5320.4 form. As such no one other than the transferee can technically have access to the item either, this includes inside your residence. If the suppressor is in your name, your husband can use it, but you must be present. Also, you'll need a copy of the approved form whenever you take the item out of your residence. If your husband was to be in possession of the suppressor, without you or the paperwork - YIKES. You're in big trouble.
Now let's say you buy the suppressor and use it a lot. After extensive use they'll need repair work done. So ATF strongly recommends that a Form 5320.5 application be submitted for approval prior to conveying the firearm for repair. Another Form 5 should be submitted by the shop doing the repair to return the item to the customer. Also, depending on the repair, the suppressor may have to be re-registered and another $200 transfer tax paid. You should also be aware that some shops licensed to work on ATF items may not be honest and try to ding you for additional fees and such.
And just when you think it can't be anymore complicated. You need to fill out a ATF Form 5320.20 for permission to move the item to another address even if you move from one apartment number to another at the same location. They want to know EXACTLY where it is. If I recall the 5320.20 doesn't even mention suppressors, however the person I dealt with at the ATF said the form has to be submitted and approved.
And if you think that's difficult...you may live in a state that allows civilian possession of a suppressor, but the CLEO, (chief law enforcement officer) doesn't think it's a good idea, and may not sign off on the forms. ATF and DOJ are preparing to drop this requirement for Form 1 and 4 transfers. But I have no idea if they've done so at this time.
The process is made to be as costly and time consuming as possible. After dealing with a number of establishments who deal in NFA weapons I've come to the conclusion (sorry about using a broad brush here folks) that many of these places don't know the laws, convey false and imprecise information, and will wheedle as much cash as they can from you knowing that you're as
confused about the subject as can possibly be.