Data access in linked containers/services

Is it possible to have access to the code being checked out during build for linked services too?

Use case:

I have some behat/selenium tests which uploads a file. As the selenium container is a linked service, it does not store the file itself, therefore the upload fails.

CI docker (code repo with file to upload @ /builds/group-name/project-name/upload.me) --> linked to selenium docker with browser (get's instructed to upload /builds/group-name/project-name/upload.me which does not exist inside this container)

As the /cache directory isn't neccessarily shared (probably on different runners), this won't work. Also, modifying prebuilt images to contain the files is no nice solution.

How does step 6 in How Docker integration works is performed? Can we use the same thing for linked containers somehow?