S.W.
To answer your question - no, it's not normal for men to hang out with friends every night after work or have affairs. But, I think you should step back a minute and reread your own post. Focus especially on this sentence:
"We both have feelings of resentment that one of us works more than the other one, which is probably not true, but I do feel my job is a lot more stressful than his."
Clearly, you think your job is harder, more stressful, etc., even though you're trying (unsuccessfully) to convince yourself that you both work equally hard. I'm currently in a situation that is the reverse of yours. I am the primary income earner for my family while my husband works part time (2.5 days a week) and manages our household the rest of the time. For me, it's stressful knowing that our home DEPENDS on my job and my income and sometimes I feel like that entitles me to more "fun" after work or on the weekends. Does this mean my husband doesn't also deserve some "fun"? No, of course not. Does this mean I have earned the right to completely disregard my family obligations (including my marriage vows)? Absolutely not!
Sounds to me like you both need a night off every once in a while when your work/family obligations are put to one side. How about you each pick an evening next month where he can hang out with his friends and you watch the kids and then vice versa. That doesn't mean you're giving him permission to do whatever he wants (i.e. have an affair - that's just crazy). But, it means he can go out, have fun, and not come home to an angry wife with a "honey-do" list a mile long.
When was the last time you took a vacation, just the two of you? Maybe that is in order sometime soon as well. You don't have to go far - maybe a weekend at the Gaylord Texan or Four Seasons - is all you need.