Your bankruptcy should not appear on your spouse's credit report anywhere. This is true even if you have joint debts. Be careful, however, because credit reports often have mistakes. A bankruptcy will appear on two places on your credit report, the "public records" section, and the tradelines of each individual account.
BANKRUPTCY AS A PUBLIC RECORD ON CREDIT REPORT
The public records section is where things like judgments, bankruptcies, and tax liens appear. The bankruptcy is listed on the public records section of the credit report only of the person who actually files for bankruptcy. Married couples do not share credit reports according to this article from Experian. So if you file a bankruptcy without your spouse, then the bankruptcy will not be on his/her credit report.
BANKRUPTCY ON EACH TRADELINE
The tradelines on your credit report are the entries for each credit account that you have open, or have had in the last few years. There is one tradeline per account, and it includes information like the name of the creditor, the payment history, and the current status of the account. The current status is things like "charged off, sent to collections," or "included in bankruptcy." This article from Experian has more information about tradelines.
When you file bankruptcy, each of your open credit accounts (tradelines) should say "included in bankruptcy." If the credit account is joint with your spouse (or anyone else), the joint accountholder's tradeline should NOT say "included in bankruptcy." This is because the joint accountholder did not file bankruptcy, and still owes all of the money. A bankruptcy discharge only discharges the debts of the person who actually files the bankruptcy, not cosigners or joint accountholders. The reason that lenders ask for cosigners is that they are afraid that the primary borrower might not be able to repay the loan, so they want someone else to pay it in the event of a bankruptcy or insolvency.
Photo credit: © Marko Volkmar | Dreamstime.com