Can you give some specifics in what you were arguing about? Using the word betrayed makes people believe that there was a betrayal, and if there was then if you don't mind elaborating on what it was. This way we could give you the best advice possible. One thing you have to know about men, they aren't mind readers. So if you are feeling a certain way, then you need to express it to him. The silent treatment never helps in a relationship. All it does is cause resentment and distance. Communication is key to a healthy relationship and so you can begin with sitting him down and telling him how you feel without laying full blame onto him. He will shut down completely if you start the blame game. All I would say is "When you said this, it made me feel like this". I've been with my husband for almost 9 years and feel like life is too short to remain angry for days on end. An apology should be enough and he needs to remember not to do what he did again. But I don't know what he did exactly so it's hard to give advice.
I would agree with all the above posters.
My first impression/opinion after reading your first post was someone or someone should leave because the marriage is too weak to salvage.
In my opinion, it is beyond marriage counselling.
Reading through your profile, it's hard to imagine your husband is going to be around much longer.
He's had to give up his family because of the friction between you and the family, (don't know why that started) and he' taken "full blame" for that.
Now, you and he have had a fight and he's once again apologized and taken full blame, but it's not enough.
He seems too weak to stand up to his family, and too weak to stand up to you, but I don't think it will be long before he's had enough.
You had a big argument? You are using words like betrayed -- an argument is not betrayal, though. (It's pretty natural for a couple under stress to have arguments.) Or are you saying the problem is that he cheated with another woman? It's kind of hard to understand if you are being childish and expecting him to bend over backwards over a basic argument that is natural in the situation, or if he has done something really, really bad and is not acting correctly to provide closure about it. Perhaps you could explain a little more about the situation. (You don't need to say "he said this and I said that," but you could give a general description of the problem.)
I do think that when a couple is under stress, it is pretty normal to fight. The question I have in reading your post is why you are holding a grudge if he is acting concerned and asking if you still want to be married.
Why is his apology not enough? What more are you expecting from him?