It's not about giving up your independence, it's about sharing household costs fairly.
Too many mothers take the lion's share of the cost of raising DC well as all the extra work and have little money to spend on themselves, while their partner focusses on his career, pays into his pension and has a lot more money to spend on himself while his female partner has less spending money because the 60/40 percentage contribution split leaves him with more personal money and she spends most of her smaller share on DC anyway.
That's why people suggest paying all income into a joint pot, that is for all joint costs, so bills, joint savings, family spending like grocery shopping as well as all DC costs like clothes, clubs etc.
Then both partners get an equal amount of money for themselves in a personal account to spend/save solely on themselves as they wish.
But to answer your question about the CB, the fairest way is for it to be paid into a joint account and any repayment to also come out of that account, with the remainder being part of 'family money'
You say your DH earns more than you and is secretive about money. I'd bet my mortgage free house that your current way of managing money advantages him to your detriment. What pension do you have compared to him? What about savings and investments? How much money do you have to spend just on you, compared to him? How much say do you have on joint large purchases like holidays, home improvements, cars that each of you drive?