How can a single GIT repository be set up for multiple .NET Solutions

You're not being really clear on how this code is managed when you develop it, but I am presuming you are using Visual Studio 2013 and want to add both solutions under the same git repo.

Short answer is, that can't be done. Not if you are going to manage your code in Visual Studio 2013, anyway. 1 solution = 1 repository, always.

In that way, git handling in VS is different than had you used TFS, which allows you to manage code by workspaces. Git uses a different assumption.

That said, there's no harm in having two different repos. Since that's the way you treat the project, it makes sense to have different repos.

However, if you MUST have both solutions in the same git repo, the way you would do that is to not use VS to manage the source control. Instead, you would put both solutions in the same parent folder.

Then you would apply git source control to that parent folder using a third-party tool, such as SourceTree.

This would require you to use SourceTree or the like to manage your commits and remotes, and would become unwieldy if you have a lot of people working on the same repo. But it is doable.

My best advice: Just use two different repos. That's your development pattern, anyway. Don't tamper with success.