I built a sample with MusicStore. It doesn't use ISS (but could), just a self-hosting ASP.NET Core MVC app: https://github.com/friism/Musicstore/
You might find the SQL Server Dockerfile interesting (hopefully it'll be an image on Hub soon): https://github.com/friism/MusicStore/blob/master/docker/mssq...
Here's now to run it:
docker build -t sqlserver:2016 -f .\docker\mssql-server-2016-express\Dockerfile .\docker\mssql-server-2016-express\. docker-compose -f .\src\MusicStore\docker-compose.yml up
IIS runs in both nanoserver and windowsservercore-based containers. Here's and IIS sample image (I suspect Microsoft will be updating it soon): https://hub.docker.com/r/microsoft/iis/