My Dad was a serial cheater and my parents stayed together too.

They lived in separate rooms and my Mom had a successful career and many friends. My Dad worked in the Middle East for decades but they never divorced. In fact, after a few rocky years at the start, they settled down as friends.
My Dad couldn't even be faithful to his girlfriends, but after my Mom died of a heart attack at 53 he refused to remarry because he "only had one wife for life".
I thought the whole situation was nuts but it worked for them. There are countless variations of this scenario in homes all over America. Most of our friends thought I came from an ideal, loving family...looking back I guess I did!