This really is going to be a case of actions speaking louder than words.
You say your DH will bale you out with 6 months belt tightening? Are you able to make any contributions?
Depending on what the CC debt was for will also impact - if it was non-essential purchases (bags,shoes perfume etc) - selling some of them to raise funds even part used perfumes raise quite a bit on ebay - I made 250 selling a few bottles, (you won't however, get what you paid for them) but that 250 or whatever, can go directly on the debt or free up money from the houskeeping to ease the burden. Just the action of doing this will show you are committed to helping clear the mess you have created.
Unfortunately, what has happened is a breach of trust, so to build that trust back, will take time. I know you are sorry, you will have even told DH this, but you now have to show him you are sorry.
If he is going to be working OT to raise extra money, making him a nice meal for when has some free time, or even allowing him a drink out with friends (perhaps paid from money you raise either selling stuff or working), will show you appreciate what he is doing to essentially save your home.
He is not going to be in a good place for a while, as he now has the debt burden and may feel he is working/going without things for something you have done. If that is not managed carefully, resentment takes hold and that can be catastrophic to the marriage.