Generally, "business" logic can be shared assuming you structure your app
such that presentation and business logic are kept separate.

My guess is that you need to refactor your code such that as much common
functionality is encapsulated in real "business" classes. These classes will
not know about presentation stuff, but are used by the presentation classes.

Take a login form, for instance. You would probably make a:
desktop/login.aspx and desktop/login.aspx.cs
and also
mobile/login.aspx and mobile/login.aspx.cs

Both of these pages will have text boxes for username, password, and a
button to login. The event handler for that button click event on each page
should probably instantiate and call a method in a third business class:

void button_click (object sender, EventArgs args) {
   LoginLogic loginLogic = new LoginLogic();
   if (loginLogic.LoginUser(username.text, password.text)) {
       Response.Redirect(loggedInPage);
   } else {
       Response.Redirect(failedPage);
   }
}

that third class (LoginLogic) will have all your real business logic. Your
presentation classes, then, can hopefully be kept quite simple.

You can go further and create a common presentation helper class that can
take on even more of the common functionality.  For instance:

public class CommonLogin {

   private Page currentPage;

   public CommonLogin (Page page) {
       currentPage = page;
   }

   public void HandleLoginClick(sender object, EventArgs args) {
       LoginLogic loginLogic = new LoginLogic();
       if (loginLogic.LoginUser(username.text, password.text)) {
           currentPage.Response.Redirect(loggedInPage);
       } else {
           currentPage.Response.Redirect(failedPage);
       }
   }
}

then in your two aspx.cs pages, you'd create an instance of CommonLogin, and
add event handlers to it. something like:

   button.clicked += new EventHandler (commonLogin.HandleLoginClick);

Please note, all above code was written in the e-mail client, so I'm sure
there are many syntax problems. Hopefully, though, it will help you get
started.