Credit report showing debt consolidation

Interesting question. What shows on your report is that you are using a service to pay your debts. Some lenders take a dim view on this,some don't. What you have to ask yourself is which looks worse. A bunch of charge offs and possible judgements or a debt service. I would think that if you ask a lender to do a manual review instead of a score model that it would be positive for you since you are showing them that even though you had problems, you are still handling your bills.
About your husbands name on account. I would need more info on this. Is he a responsible party or only a user and do you live in a community property state?

You use a debt consolidation program, probably because you can't manage the payments on your own and can't pay the high interest rates. This program will be reported in the file until you have completed the plan. The lenders viewing it will see it in different ways. Most will think that you are taking care of your debts while a few may want to see your debts completely paid off before extending new credit to you. You have to negotiate with other good factors in your credit history and giving them the assurance that the present debts will be paid off as per the plan.