When the time is right, I think he needs to be slapped around a little bit (emotionally speaking). If he were sitting in front of me I would carry on something like, "So what makes you so high and holy that you can't make a serious mistake? What elevated you so far above the rest of us humans? What makes you so special that there is no forgiveness for you?" "Are you trying to atone for your sins, by being beyond the pale of forgiveness?" (if he is Christian, or not opposed to Christianity) I would add
, "You know there is a whole religion built around the idea of forgiveness, and grace, it's called Christianity, ever heard of it? Are you so special it doesn't apply to you?" and then I would punctuate with something like, "last time I checked you have to squat down on the toilet just like the rest of us, so why don't you get off your high horse and get on with being human and get your butt home and get to work on fixing things instead of acting like your supposed to be above or beyond?" If you couldn't tell I think drastic situations sometimes call for drastic actions. Though he is acting contrite he is really self absorbed in a self-pity party ("woe is me look what I've done"). I would also insist on a complete physical exam to rule out physical causes for depression, and I would consider and check for hypothyroidism and other hormonal imbalances, (these are not always identifiable by standard lab tests). When he is feeling a little better I recommend you push the envelope a little further by asking him about what is lacking in the marriage that he was getting filled with his extra-curricular activities. This will be difficult to get him to articulate and difficult to hear but could be helpful in the "building a new marriage" dept.
If you want more information on the effects of hormonal imbalance on physical and emotional health you can see
Last thought, don't baby him, if he was big enough to go find a poor solution to his marriage and life problems by having an affair he is big enough to do the repair and rebuilding work needed (including facing his wife's family).
If you were looking for some serene, and gentle ways to coddle him, I have surely surprised you. Instead I am suggesting that you kick (emotionally speaking) a good man when he is down, he will probably get back up.
Best of success to both of you.