We skipped the childbirth class because I decided to have an epidural and I personally thought it would be a waste of time learning breathing techniques.
We took a class called "Caring for You and Your Infant" the teacher went over post-partum care for me and general things to expect (types of poop, caring for the bellybutton, circumcision care for boys, etc) and we were shown how to change diapers and give baths (I hadn't changed a diaper in FOREVER and my husband never had, neither of us had given a baby a bath before). The second half of the course covered growing stages and caring for an older infant (teething, sleep training, baby food).
There was a powerpoint presentation on the screen that we were all given a copy of to take notes and ask questions, it was a great forum to ask "stupid" questions, we were all first time parents and one couple hadn't ever even held a baby before, so there were lots of those.
We were both really happy we took it, it was very informative.
We still want to take the CPR course, just in case.
Check with your health insurance before you pay for any classes, some of them might be covered after the first of the year when the Affordable Healthcare Act goes into effect.