Sorry lola, I am in complete agreement with Puppy. Your H has continued to cheat and lie to you. Unless/until his actions over time prove to you that he is no longer seeing OW and is doing everything in his power to make amends and become a better person I would go dark at the least. If you continue to chat and be friendly with him you are enabling his cake eating.
If you love somebody, set them free. http://tinyurl.com/2empx2g