If you are working, I don't see why he should complain about the $, unless you as a couple, have made a decision to cut down on spending. I mean, if you can't afford it, you shouldn't spend it, but if it isn't going to affect you buying necessities, then I would have an honest discussion with him and tell him you are going to do it. Maybe you could cut back elsewhere?
A few years ago I signed up for personal training at my gym (700.00 for 3 months). I was working, making good money, high 5 figures. I didn't feel any need to ask for permission, even though we share our money. I wouldn't do it now, though, because even though we can live very nicely on my husband's salary, that is something that I don't have to do, even though it would be beneficial for my mental and physical health. My good friend is working with a trainer now and I really want to, but it's not going to happen.