Two things
They can try to cook/do housework together - i.e. he helps cut veggies or wash them or something while she actually cooks. But I think the main problem is he doesn't WANT to help, which I think is disrespectful. She could do the passive aggressive thing and not cook either because she finds it too "boring" to do alone as well and see what he does.
Men who make less than their wives tend to do less around the house as well. This is because they feel that it is a blow to their ego, and then on top of that helping wife with menial labor is even more blow. They kind of resent that their wife is making more and so don't want to help. this was a study done a few years ago. And it is by no means all encompassing.
Her solution, I know it will not be well taken by most of the members here, is to hold off on the classes until later. How do you think her hubby feels when he is expected to do housework because she is going to classes that will help her make EVEN more than him? He will feel emasculated. His feelings are not right, and the situation does not work both ways, but I think it's making him more and more resentful, and less and less likely to help out and eventually it will lead to more problems. So wait until he climbs up the corporate ladder and makes more than her. Isn't their marital bliss worth more than a few extra $$ at the end of the month?