If you found out that you're husband/wife betrayed you, and you forgive him, would you easily forget what he had done?
Forgive is supernatural and it requires you to walk in an attitude of forgiveness if you are going to live with this person. Forgive one another many times and handle negative emotions responsibly by dealing with one issue at a time.
No. You can forgive but probably never forget.
You will never forget but with time and attention from him/her you will think about it less and less and just move forward. It also depends on how severely he/she betrayed you.