Here\'s what I\'d like:
REPO-A
/.git
/otherFiles
/REPO-B
/.git
/moreFiles
I want to be able to push all of REPO-A\'s
Yes, you can do exactly what you're asking with the file hierarchy you drew. Repo-B will be independant and have no knowledge of Repo-A. Repo-A will track all changes in it's own files and Repo-B's files.
However, I would not recommend doing this. Every time you change files and commit in Repo-B you'll have to commit in Repo-A. Branching in Repo-B will mess with Repo-A and branching in Repo-A will be wonky (trouble removing folders, etc.). Submodules are definitely the way to go.
I have always used symlinks to maintain two separate and distinct repos.
You can achieve what you want (that REPO-A repo contains all the files, including those in folder REPO-B instead of only a reference) by using "git-subrepo":
https://github.com/ingydotnet/git-subrepo
It still works if some of your contributors don't have the subrepo command installed; they will see the complete folder structure but won't be able to commit changes to the subrepos.
It sounds like you want to use Git submodules.
Git addresses this issue using submodules. Submodules allow you to keep a Git repository as a subdirectory of another Git repository. This lets you clone another repository into your project and keep your commits separate.