Sounds like you are drowning in a sea of intense isolation. I don't even deep down believe in my own mind that this feeling of being alive and like you matter has anything to do with him being of the opposite gender, I believe it's due to the loneliness that you must feel.
How young are your kids? Must be quite young guessing by the lack of being able to find a sitter comment. Your husband must realize, no?, the importance of the mother of his children needing some down time?

Sending warm thoughts.