Can I fix my husband’s papers even though we have a confidential marriage?

"Confidential marriage" is not a legally recognized term. If by that you mean that your or your husband are genuinely married but your and/or his family members are unaware of the legal marriage, then generally yes, a couple still may succeed with a marriage-based adjustment of status application. In that instance, however, you may expect the USCIS to require a particularly strong set of documentary evidence to show you and your husband are living together in a bona fide marriage notwithstanding that your parents did not attend your wedding and do not know about the marriage; it also may be helpful to be prepared to explain why a couple decided not to disclose their marriage. Of course, there are many additional details that determine immigration eligibility. There really is no substitute for you and your husband to consult with an immigration attorney who, after learning all of the relevant information, could advise about eligibilities, options and strategies to attain your goals, and who then could offer legal representation in the often complex application process.