Should a married man and married woman be chatting on Facebook?

Yes, if the subject matter is appropriate. Intellectual discussions, or discussions about work are entirely appropriate. The interchange of ideas is independent of gender and does not cross boundaries of intimacy.
However, if the chat discusses intimate details of one’s relationship or sexuality, it becomes a potential threat to one’s marriage. Then, it should be discontinued.
If you think you cannot remain faithful in marriage, then don’t enter into it.

A man has been left confused and in total shock after discovering the chat his wife had with a married man – this said man upon discovering the chats, then took screenshots of it and shared it online.
As can be read from the chats, the woman belittles her husband and says she wondered what she sees in him in the first place they got her married to him – and as can also be seen, she has two children for him.
Saddened by this incident, the man took to Facebook to share the screenshot, asking readers what his fate will be with his wife of 9 years.