You can group the visits under any Channel that will be easier for you to analyze and manage.
However, I will recommend grouping under
utm_medium=email) with the source pointing to the third-party (
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
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.