He may just need time. Sometimes it's so overwhelming to them they just can't deal with it full on, so they'd prefer to go about their routine. I know it doesn't seem like it, but one month isn't very long in the grand scheme of these things taking 2 to 5+ years to recover from. Some say there's a nice anger phase around 6 months.
If he does talk about it in MC, then it just may be that that's where he feels safe doing so and, since there's no hurry (right??), then talking about it weekly is perfectly reasonable. And if you're worried about delays due to summer vacations, realize the gift of even *having* summer vacations with him. There's no timeline for healing, or talking about it, or when you can stop walking on eggshells. But time really does soften things. You may not notice from one day to the next, or even week by week...
Different people deal with things in different ways. So it may just be his way. In the meanwhile you work on you. Every day he's willing to "try to try" is a gift.
In my early days I would try to read to my BW from the plethora of books I purchased on the subject. For a while she listened, but one day she said "Stop reading to me, it's depressing." So I did.
The affairs... Painful.
The reminders/triggers of the affairs... Painful.
Talking about the affairs... painful.
I'm sure just looking at me and hearing sounds come out of my mouth was painful to her for a while. Little old saintly compartmentalizing me, now the most hated person in the universe. Me? Really? Yep. I lied to her face and had sex behind her back.
But, 3.5 months later, we talk. we laugh. We live. Because life goes on, and after a certain point, we have to live that life and stop feeling sorry for ourselves to the point where we're consumed every minute of the day by what we did.
You cannot control how he thinks or feels. He's his own person and he will heal in his own way and in his own time. We waywards very much want "to fix" things and find a solution, but the solution is letting go. Live your life honestly, and authentically. Don't just "act normal", *BE* normal. Be yourself.
A quote that I like to share from time to time:
"When something bad happens you can either let it destroy you, define you, or strengthen you."