Im so sorry Lesky that this happened, betrayal injures the heart so deeply and compleatly.
I can not speak to what your husband should do, for him, all that can be done is to give him to Jesus compleatly, and pray for him.
My husband betrayed me several years ago, different stuff, but needless to say, my heart was not only broken, but crushed.
I thought at firstt by showing how much he hurt me, he would see and be sorry, wanting to repair all.
Saddly this had the opposite result, instead he saw himself as the victem, making the situation worse.
Thankfully Jesus showed me how important it is to forgive, and give him to God.
First the forgive, I saw Jesus on the cross, not just for me, but just as much for my husband, trully a humbleing mpment.
Jesus also showed that by holding on to the hurt, instead of forgiving, it leads to bitterness, fist signs are the highs and lows.
I learned in Jesus that I needed everytime my husbands actions started to eat away at me, that I had to speak forgiveness and praise to God for his care and salvation.
The give part is really part of the forgive, you have to compleatly give him to God, no more thoughts or words on how your husband should be.
You give him in Jesus to God, every time you think or start to think, give him in Jesus to God.
Pray for him also, alot.

Then love your husband as called to in scripture, I know this sounds redicules, I thought so myself when Jesus set this before me.
But when we forgive, think, speak, and live in faith what God asks us to, His power, glory, healing, and perfect love is perfect and amazing.
Long story shortened, my husband trully came to accept Jesus into His heart, he asked my forgiveness, and every day since then, works to win my heart.

He still is not perfect, but I praise God for the perfect in him, Jesus!

There are no garrentees, but when one does all asked in Jesus, then one can be confident that everything one has done is Jesus, has been done.
Because perfect love is learning in Jesus how to give love, not just recieve.
Also, God will in Jesus give you all you need as well.
you both are in my prayers in Jesus.
Hugs and God bless
pickles