As to the moral issue, if his wife is really this lady's best friend, she probably already knows about the affair. Spouses in law enforcement and other similar fields are *expected* to keep 'secrets' from their spouse. His spouse should be well used to not hearing everything about her husband's day.
Professionally, he signed a confidentiality agreement at the least and may very well have had to take an oath. It can not only cost him his job to violate that agreement, it could result in criminal charges.
He's only in a tough situation because he's emotionally involved in it. If this were a casual acquaintance he would not think twice about saying and doing nothing.
Sarah