You can group the visits under any Channel that will be easier for you to analyze and manage.
However, I will recommend grouping under Email (utm_medium=email) with the source pointing to the third-party (utm_source=<thirdparty_name>)
Reason
In the future, you may have to analyze conversion rates from different sources and mediums. You may also have to compare the conversions between emails from your newsletters against the third-party ones. In this case, grouping under Email will help you easily compare between sources (yours vs the third party) from the same medium (email).
Note: Though you use banners within an email, I think the foremost factor contributing to whether a user visits your site from the newsletter will be the open rate (good subject lines, the credibility of the sender, etc.,). Only if a user is going to open an email, he will even see the banner. Hence, I think medium email should take precedence from a logical viewpoint.