I think that the process and act of forgiveness is the same for all people, religious or not.

It's not always easy to forgive someone. It can be hard work and takes time. Sometimes its a journey of taking one step forward and two steps back.

Sometimes you have to keep on forgiving someone over and over again for a single indiscretion. Perhaps every day, week, month, however long.

I think that you can forgive someone, but still feel hurt and angry. Perhaps be completely honest with your wife.

Edit: I hope you'll excuse me for typing this also, but your wife may need to forgive you for being suicidal. It's never a person's fault for being suicidal, but it leaves family members scared. Forgiveness is a journey and process needed to be taken by everyone. I'm sorry, I just mean to say that she may understand how it can be difficult to move on. I hope I haven't been too stupid or offense.