I think it depends on the type of class you're taking and your personality. If you are doing a Bradley method class, that focuses on partner coached childbirth so you would need the person at the classes who will be your birth coach.
And I disagree with the comment about what help a husband would be (something about an ice cube?) while you are in labor. If you are choosing to have a medicated birth, that may be true but if you are going med-free then a birth partner can be very beneficial to some people. Someone to remind them of breathing techniques, labor positions or positive imagery can be the cornerstone of a positive birth experience. But it's not necessary for everyone. I labored completely alone for my second child and preferred it that way but many women need someone there for support and encouragement.
So, I really do think it depends on the class and your birth preferences. I wouldn't forgo the class if it was impossible to have my birth partner present though.