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In cases where both spouses are listed on a credit card even though only used by one the effect of negative (or positive) behaviors will impact both credit scores. No one can add their name to the credit score of another without the consent or use of joint accounts. There is no way to remove a link (other than divorce or individual bankruptcy) between the two of you. Somewhere along the line your credit activity crossed lines. It could be as simple as one of you paying the others credit card bill, a joint bank account (even a savings account) or a joint mortgage. If your husband was somehow able to get his name added to your credit card you will need to call the card company and either cancel the card or have his name removed since you did not authorize this. However, it can be construed as bank fraud by him. That is criminal so you will need to think this through carefully.
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The main problem that would affect your credit would be the high balance. The more unsecured open tradelines you have, it will lower your score. Especially if you have balances on them. If you are removed from the card and the tradeline is removed from your record, then it should have a positive affect as opposed to a negative. If I can assist any further, let me know...