Adams has been accused of "improper conduct and insulting words" aimed at referee Mike Riley moments after the half-time whistle in the recent home defeat to Birmingham City.
Thatcher has been charged for an alleged stamping offence on Arsenal midfielder Freddie Ljungberg during the 1-1 draw with the Gunners at The Walkers Stadium.
"We are appealing against both of the charges," siad Adams.
"I stand by what I said at the time, that I didn't use any foul or abusive language and, believe you me, I didn't use any 'insulting words'.
"I may even call in a lip-reader to back up my claims. That is definitely one avenue that I may go down to try and prove I am innocent of the charge.
"As for the charge against Ben Thatcher, it is a nonsense.
"The charge came out of the blue and, having examined the incident from all angles, we will be fighting that charge. If he receives a three-game ban for that, then it will be nonsense.
"We will be using video evidence as regards defending both charges - if we are allowed to put it forward."