Azure websites deploy specific web project
Now it is as simple as using App.Settings instead of a .deployment file.
This also allows for multi-project solutions in one Repo, so for example, if you have a WebAPI and a Web App in one solution you can configure an Azure Web Site to deploy a specific project. like so:
I have tried this and works a treat.
You will need to work with 2 different branches combined with a .deployment file.
So the first branch could have something like this in the .deployment file:
[config]project = WebProject/WebProjectA.csproj
And branch 2 something like this:
[config]project = WebProject/WebProjectB.csproj
I came across a good blog post that describes how to do this using a custom deployment script. It is a bit fiddly but is a workable solution until something better is added.
http://blog.amitapple.com/post/38419111245/azurewebsitecustomdeploymentpart3
Edit:
This one is even better and allows you to do it with a couple of extra files at the route of your repo:
http://www.devtrends.co.uk/blog/azure-web-sites-git-deploy-for-multiple-project-solutions