Hi clement,
You definitely can create sub-site in your team site. Could you please capture a screenshot of the tree view which confuses you and post in the forum (please mask the private information before you post them)?
I have attached a screenshot which might shows a bit more clear in the structure.
You can find that I have 4 sites in this site collection, which are Team Site, Website, Search and SubSiteUnderTeamSite.
When I go to the SubSiteUnderTeamSite and click the “Navigate Up” button, it clearly shows the structure of the site collection.
I hope these screenshots will give you a better picture.
Thanks,
Kent Gu