Gently, OW is not your biggest concern. A husband with a security clearance that renders him invisible is.
Yep. We've had a few in that situation here before. Living the life of a "secret squirrel" means he can lie and there isn't anything you can do about it to verify facts, or conversely to ease your mind that all is ok, should you suspect things and aren't sure if you're overly sensitive and wrong, or being intuitive.
If you ask questions, he can shut them down with the job excuse.
The tips given to new BS for "trust but verify' methods to receive transparency and heal the marriage cannot be used with a secret-clearance issue, or the BS of a "secret squirrel' type can wind up in legal trouble.
You can't check to see if his car is in the parking lot at work to make sure he really is at work if security clearance is needed to get on site and you don't have it.
You can't use a GPS in the car or VOA recorder in the car if the car is searched before entering checkpoint, or sometimes randomly so, and it's a risk it will be found and trouble come your way. Or if it's routinely turned in for maintenance and you choose the wrong day to have that stuff in there.
Can't use a keylogger on his phone or laptop if both are work issued, since the laptop and phone aren't considered part yours. You could be charged with a federal or state crime. Or if he's not with government, with tampering with corporate or trade secrets - business espionage.