I am trying create a single page web app combining both ASP.NET WebAPI and the Yeoman Angluarjs generator. Currently I have a project structure as laid out below
URL rewriting is exactly what you want, with a condition block to test if the file exists. The content under your dist directory is static (i.e. lives on the file system) but the WebApiApp routes are dynamic. So you simply need to test if the route matches a file that exists in the dist directory or not, if not simply let .NET handle the route. Adding the following to your Web.config file within the section should do the trick:
The second rule is optional but it means a request for the root of your site will still serve the index.html file from the dist directory, effectively making the root of the project WebApiApp\dist but still allowing all WebAPI routing.