Ok, I see a couple questions here.
The title is can mental health cause infidelity? Well, I guess in a way, it could. The underlying untreated dysfunctional traits such as need for external validation in some disorders could lead to infidelity. Still, though, the responsibility does fall on the person to recognize the dysfunction in their life and seek treatment BEFORE betraying the most important person in their life. So I don't take mental health as an excuse for infidelity.
The second question is can mental health cause memory lapses. The answer to that is a resounding yes!
I have severe PTSD. When my PTSD is at its worst, I lose parts of my memory. Sometimes, it's short term memory loss. Sometimes, it's long term.
Went to Wal-Mart the other day, remember driving up the hill talking to my friend on the phone, remember still talking to her on the phone as I got a buggy inside and headed to the deli where I got off the phone with her. DO NOT remember pulling into the parking lot at Walmart, couldn't remember where I parked, walking in, nothing. It's not the same as walking in a room and forgetting what you were there for. In those normal instances, you can retrace your steps and recall the memory. In this type of situation, no matter how you retrace your steps, the memory is gone. It's like it didn't store, didn't process. It's just an empty room when you seek the information. It's quite scary.
Oct. 8, 2010 my best friend claimed MrWNW raped her (which he didn't but that was her attempt to tell me of their ONS without claiming responsibility). Dec. 12, 2010, MrWNW asked me to move out via email. Between each of those dates, I have NO memory except one day, Christmas shopping and later giving MrWNW his Christmas gifts early. I've gone back, read IMs, emails, seen pictures the kids brought me home from school, etc. Nothing restores the memory. It's just not there.
I have other times that are similar in life. Extreme stress and trauma are when my memory gaps occur. The longest is an 8-10mo period after my rape in 2001. Don't remember much at all. Shorter gaps, like the Walmart instance, occur about 3-5x per week when my PTSD is going haywire.
It's truly frightening, but yes totally plausible. My doctors are setting me up with EMDR. Not sure if that treatment is effective for bipolar, but it apparently does wonders for PTSD. Perhaps discuss that treatment option with your husband and his doctor?