Hi Kathy
While CompleteFTP doesn't support ASP.NET membership authentication out-of-the-box, it does allow you to create your own authentication plug-ins in C# or VB.NET.  A simple example is shown below:
using EnterpriseDT.Net.FtpServer.Core;
namespace MyTestAuthenticator
{
  public class SimpleAuthenticator : Authenticator
  {
    public override void CheckUserName(IUserInfo userInfo)
    {
      if (userInfo.UserName == "myusername")
        userInfo.IsValidUserName = true;
    }
    public override void Authenticate(IAuthenticationInfo authInfo)
    {
      if (authInfo.Password == "mypassword")
      {
        authInfo.IsCorrectPassword = true;
        authInfo.HomeDirectory = "C:\\Temp";
      }
    }
  }
}
In your case you'd probably need to call the 
Membership.Validate method in the Authenticate method to see if the user is allowed to log in.  I haven't tried this, so I don't know for sure.
I hope that helps.  Please let me know if you have any further questions.
- Hans Andersen (EnterpriseDT)