Thank you for contacting JustAnswer.
I am sorry to hear about the problems you are experiencing in your relationship. As you noted that your husband was diagnosed with depression, it is important to understand that, particularly with men, depression can take the form of anger and irritability, low motivation and difficulty making decisions. People who are depressed tend to have low motivation, to feel hopeless, helpless and overwhelmed. You may find the following website helpful for more information: http://www.nimh.nih.gov/health/publications/depression/complete-index.shtml
This could explain some of his behaviors. Additionally, affairs are often a way of avoiding feeling uncomfortable feelings, such as those which come from depression. As long as someone is engaging in an affair, they are unable to put the marriage first and work on that relationship.
It is also important to keep in mind that actions speak louder than words. It appears, from you description that your husband's actions seem to indicate that he is not showing you a reason to believe that he has changed, perhaps that he has not resolved the depression or ended the affair. Patterns of behavior tend to predict behavior. Unless he shows you reasons to believe that he has made major changes and has begun to take responsibility for his actions, I would encourage you to be very careful. He would need to earn your trust back if it is to be even a possibility.
One thing I would add is that it seems that you have been doing quite a bit of emotional work about this relationship. In order for this to be a healthy relationship, we would expect your partner to do a relatively equal amount of emotional work (if you balance it out over time). This may be one way to evaluate if someone is committed to a relationship and to changing in order to make the relationship work. You deserve someone who will put the work into the relationship as well, since it takes two people to make it work. Also, I definitely believe in trusting your gut. It is often a very good indicator of red flags that should not be ignored. Feelings of love tend to be very irrational, while the gut is a good barometer of danger, both physical and emotional. I hope this is helpful and I wish you the best.