Ultimately the only way to become financially independent is to get a job. Squirreling away money means that you have the means to support yourself in the short-term if you leave but it doesn't provide you with the independence that a job/career does.
I would think that you need to look at your super and stocks - it's not unreasonable to ask that a percentage of his wages goes into a super account for you. Or you could self-manage super and invest it in stocks etc in your name. Poverty in old age is more common in women than men because so many of us are out of the work-force for extended periods (or even permanently) so women should look towards the future when doing household finances.
Also mortgage - do you have one? If so that should be in your name too. The work you do in the home is what enable him to work out of the home so assets should be jointly owned.

Also, if you want to be financially independent to strengthen your marriage that's great if you want to be financially independent so you can leave him I would think that it's undermining your marriage. Knowing that you can leave is good for a marriage - it prevents resentment. Planning to leave is bad for a marriage so you may as well leave now and claim child support and social security until you get a job.

Keeping secrets about money is not good for any marriage.