Not usually. They may try and you may have to be diligent in preventing it, but a bank account owned jointly by husband and wife is considered a tenancy by the entireties in Florida and protected against attachment and garnishment by a creditor of only one of the spouses. However, I have seen creditors try but usually a bank will not allow it if the writ is only in the name of one of the spouses. But, just to be sure, you might contact your bank and see if you can't change the name on the account from John Doe and Jane Doe to "John and Jane Doe, husband and wife." Or "John Doe and Jane Doe, his wife." That way there will be no mistaking you for brother and sister.
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It depends on how the account is classified (tenants in common, tenants by the entireties, joint tenants) and the specific wording used in the forms on the signature card and related agreements used when the account was first opened. In some cases, they cannot touch the account, and in other cases they can. Because it very much depends on the specific wording used and your unique factual circumstances, you should probably consult with an attorney to determine your specific rights and responsibilities.