Your instincts are correct if warning bells are going off. When your husband talks about his marriage to another woman, it’s a problem waiting to happen. The best thing to do, when you are in a calm mood, is to talk with your husband about the situation. Let him know that you have become aware he is talking to another woman about your marriage. 

Give him the benefit of the doubt by saying something like, "You may not realize this, but talking to another woman about our marriage is very dangerous to the health of our relationship, even if it doesn’t appear to be the case. I would rather you talk to me about the feelings you have about us. Then we can deal with things together." You might want to add a comment such as, "Clearly you’re having a strong reaction to something going on in our relationship. I really want to know what’s going on." 

Let him know that you are willing to go to a counselor, if needed. It will give the two of you a safe and neutral place to deal with these issues if they become too intense. But talking negatively about one’s marriage outside of the marriage only contributes to the downfall and toxicity of the relationship. NOTHING good can come of it!

It’s not uncommon for people to feel betrayed, devastated and humiliated after finding out about a partner’s infidelity. Many partners blame themselves, thinking somehow they were not enough of a "man" or a "woman." They believe that if they were "enough," an affair would not have happened. 

The truth is people have affairs for all kinds of reasons. Sometimes they want to feel young again or to experience that "exciting" romantic feeling once more. In other cases, they have a deep fear of intimacy. The bottom line is, regardless of the reason, being cheated on still hurts. 

The trust is never the same after an affair is discovered. An affair interferes with the naïveté of the relationship. Having said that, many couples manage to survive an affair and even become stronger once they have dealt with it out in the open. 

For both partners to move on emotionally, the affair needs to be incorporated into the tapestry of their relationship. Here are some important key points:

— Take it one day at a time.

— Don’t expect too much of yourself too fast. 

— Give yourself time to grieve your old relationship. Until you do, you can't move on.

— Work with a supportive and trained counselor to help you make sense of everything that has happened.

A marriage can be saved after this type of betrayal and in some cases become stronger, but the relationship will be different than it was before, and the healing process will take time.

It appears that you have two basic questions here, "How do I get over the affair?" and "How do I learn to trust someone who continues to hide information and lies repeatedly?"

Let’s go to your first question. Getting over a partner's infidelity takes time. It’s not something that happens over night. The betrayed partner is grieving the relationship that they thought they had versus the relationship and partner that they "really" have. Some days you might feel better than others; that’s to be expected and perfectly natural. 

Asking your husband questions is a way to come to terms with what happened. You may need to let him know that you are asking questions for that reason and not to badger him, make his life difficult or punish him. Let him know that asking questions helps you to care for yourself emotionally after what's happened and by answering them he can also help you to heal.
Many men fear going over the details repeatedly, because they worry it will re-open the hurtful wounds. In fact, it can help achieve the opposite. Eventually the details become less painful and hurtful over time. You may want to seek marriage counseling, so you can carry out this difficult emotional work in the presence of a trained professional. In the meantime, try to avoid engaging in the blame game; it never works and it only delays the healing process.

Now to your second question, how do you trust someone who continues to lie and hide information from you? The short answer is you don’t. Not everyone is trustworthy, and trust is something that is earned anyway. If your husband is not willing to change his behavior, then you need to ask yourself if this is acceptable and something you can live with. 

This may also be the time to get practical. Look at your finances and household situation. If you need to end your marriage, at least you will have thought, in advance, about the different ways you can take care of yourself.