We had already been married one year and a few months. We were living overseas at the time waiting for his visa to be approved. By the time I was ready to give birth to our first child the paper did not come and I wanted my child to be born in Australia so we decided that I come home 2 months before the baby was born and hope that he would get the paper before the baby was due. We talked every night and everything in me was telling me something was not right so I ask him and he acted like everything was good saying he loves me and can't wait for us to be a family. Well it didn't and he missed the birth of his first child. So he finally comes to Australia and I feel that something is wrong.

So one day about 8 weeks after he arrived here I come home from work, I was excited because I would tell him we are going to have another baby and I checked my computer only to find his secret email address open and I started reading all the emails to and from the woman. These emails date back to when I first left to come home and that he had asked this woman to marry him knowing he couldn't because we are still married. Telling her he loves her and planning a future with this woman she even went to where we lived to see him twice. She lives in another country and both times they had sex a few times.

My heart just broke into small pieces and I don't know how to forgive this man. We are still together it's been over a year since he arrived here and I'm still very very hurt . When I asked him he said he doesn't know why he did it. His excuse was I was too jealous and always used to argue with him and he wanted to see if all women was like that. He said that all the time he was doing it he was always thinking of me and he never lost any of the love he had for me. And even today he says he loves me and only me and always will. I have asked him if he loves her he said he never did he would tell her that to make her happy he said he did care for her but never loved her.

We are still together but I really don't know what to do I'm here because of our 2 children I'm an honest faithful woman I did not deserve this. I do love this man I have never love anyone or anything the way I love this man. We do go to couples counseling. It was his idea because he said he didn't want to lose me. I JUST WOULD LIKE SOME ADVICE PLEASE!!

One of the standard first pieces of advice is to get the cheater to agree to couple counselling, and surprise! Your hubby suggested it. So that is a good sign.
Your title question is how do we move on. I wonder if what you really mean is how do I move on. You are the one suffering, not him. Any suffering he claims to be going through is not justified, even if you were naggy, and those reasons he gave for what he said to her are so lame as to not need addressing.
But this isn't about him. It's about YOU! He is who he is, he did what he did. What do YOU want to do? Let's say you want to get past this for the sake of the children, so how do you live in the same house with him?
I don't think there is a single solution. It's a process. Counselling is supposed to teach you how to communicate with each other, not solve your problems, or pick sides. You are taught how to talk and then you are sent home to do it.
What would I do, with small children? I would treat him formally. When the kids are around, I would lighten up, but when alone with him, I wouldn't recreate all the grief or nag, I would act distant, like he's a visiting cousin you have never met. He has tremendous work to make up for what he did, but don't make it easy for him to say that all your recriminations are driving him away again.
If you can't do that - all you can do is divorce him.

I believe that you are a faithful woman, actually you are too good for him. I see that you still love him and respect him no matter how low he went, you sure are too good for him.
There is no wrong with second chances, but keep your distance and be firm. He obviously is not aware of the destruction he caused. When he made this mistake he was not thinking of you sincerely and respectfully or even your children and future. But you did, what a wonderful person you are. I say trust in God and rely on him, pray for those who bring you down and you will be rewarded.

You can make it work, but he will have to understand it will take time, and you will have to be willing to try and make it work.

Counseling is needed. While not an excuse, many men who do cheat ( most don't) do so when wife is pregnant or out of town for a few months.

It will take time and work and a lot of patience to let the healing process work. Maybe even years with the counseling. Knowing this be prepared for the long haul.

Good Luck.