I created a solution a while ago that contains a Web API 2 project (provides JSON data to mobile devices) and a Class Library (includes my data access services).
The Web
This 2 projects are independent from each other like 2 different applications even if they are in the same solution.
To succeed what you try to achieve you have to:
1) Deploy your MVC project to www.example.com
(main virtual application).
2) Deploy your WebAPI project to www.example.com/api
(api folder is a virtual application). Don't forget to remove api
from your WebAPI routes (other wise you have to use this route www.example.com/api/api/controller
).
Doing this you can acces independently both projects in the same url.
For NInject part, you can register again the services in the MVC project. Another solution will (which i recommend) be to make a class library project and register there the services after that you reference this class library in both projects.