You can only add collaborators to your repository. It cannot be “co-owned”.
But when someone is added as collaborator to a repo, that repo will be listed in the Your Repositories section ( but the username will be the owner username only)
The only way for doing what you want is to fork the repo and collaborate through pull requests.
Note that you can create an organization ( https://github.com/account/organizations/new ) and achieve a bit of what you want.