To answer your question, yes. A joint credit card does show up in your credit report and does contribute to your credit score. This is because you are liable for the balance of that card and are responsible for ensuring it is paid. In general, joint credit cards are indicated as such on your credit report, so banks may know that it is a joint credit card.
Whether or not the bank cares about the fact that this is a joint card or not is up to them, though I have not heard of an instance where a bank denies a loan application on the basis of joint credit card history.
However, this is not necessarily the case if you are an authorized user on a credit card (your comment suggests this is your situation), in which case the card may or may not contribute to your credit score/worthiness depending on the policies of the issuing entity. This is because most policies are set up such that authorized users are not (legally) responsible for the balance of the credit card (but are simply authorized to make purchases with it). Thus it follows that being an authorized user doesn't necessarily contribute to proving you are capable of handling credit.
Make sure you're certain of whether you are an authorized user on a credit card or if you are a joint owner of that card. Beyond the question of applying for this loan, being a joint owner has additional implications for your obligations as a credit card holder.