I read an article today with the word "everyman." I'd not heard it before, though Shu had. It must be because I am female. I notice there isn't an "everywoman." Seriously, is this a common word, and I've just missed it?

It's not that common. Although it is the name of a character in a 15th century morality place it didn't come into general use until the early 20th century. I have also seen 'everywoman'.

Yes, I see that "everywoman" is in 10 dictionaries from Onelook, but I haven't seen that either.