We have been working closely with Xamarin, who provide a great solution for using C# and .NET to build apps for iOS and Android. You can read Soma's TechEd post, where he specifically talks about Xamarin and this scenario.
The Xamarin solution is a native platform solution. You build native UI with Xamarin, as opposed to a write-once hybrid UI. You can, however, share all of your business logic across iOS and Android apps. The same is true with Windows apps, which are supported by Visual Studio, not Xamarin.