This answer suggests that one should create a new project for Umbraco content management alongside the existing MVC application. I have created the new project as suggested, and installed Umbraco into it through NuGet.
So now I have 2 projects, one for my MVC application and one for CMS. Both are working as expected, meaning that I can add contents through the Umbraco UI after building the newly created Umbraco project.
My question is, how can I query the content from inside the MVC application in order to show the manageable content on my views? It seems that it can be done through the Umbraco REST API, but as both databases (for the MVC application and the CMS application) will reside on the same server this seems unefficient.