is it okay for hubby to flirt with others?

Hubby and me are currently going through marriage counselling session. Why we went through these is because I found flirting messages that he sent with a woman and when I confronted him, he says that's all because I did not give him regular sex life and he is just venting out. No actions done. I agree, after pregnancy of my #1 and now with #2, I always felt tired and rejected him when he initiates. Or rather I originally have low sexual drive. Is that a reason of betrayal? He also says I have invaded his privacy which that's something that he cannot tolerate. I thought counselling can helps to make him understand he is wrong in that aspect for the messages and the most ridiculous thing is he told the woman he still not convinced our 2 year old son belongs to him. I wanted to do DNA to prove my innocence and give justice to my Son but he wanted to ask me pay first cos he does not have enough $. I often think why am I deserving such a treatment just because I did not attend to his sexual needs? Now my question is why will he think his is totally not at fault? I cannot rationale this and he told the counsellor the reason why he comes for the session is just want to see how the counsellor resolve my low sex drive issue and not to save the marriage for our differences and no trust? If my issue is settled, everything will be back to normal and he simply did not think on how bad I was hurt about the betrayal and injustice about doubting our Son is not his. I kind of helpless too cos I am 6 months pregnant with our Daughter now. If there is any daddy advice addressing my question will be appreciated too. Sorry for the lengthy post.