We're looking for the mixed authentication solution, which will be
seamless for both internal and external users.
The way we would like to accomplish it is:
1. Both internal and external users are accessing the same URL: www.myapp.com
2. If the user is internal user and system passed his/her token
correctly then the system automatically authenticates user with
Windows Authentication
3. In the case the user is external, no windows authentication form is
displayed and instead the user is redirected to app login form.

Is there any way to make this simple?

Bypass Authentication
Serializing credentials and reauthenticating. How?
PrincipalPermission, getting started
How to interface to Certificate Authority from C#
Unable to copy file to a shared path on remote server
CAPICOM and .NET signedCms.CheckSignature
CAPICOM keylength for 3-DES
How to track down source of crash + Event log error?
How to get Windows user name of a 3rd party application in dotnet?
Embedding Software Registration Info in Win Registry