Yes, it is possible. What you want is a C++ web framework. You could start by looking at CppCMS—a Free High Performance Web Development Framework (not a CMS) aimed for Rapid Web Application Development.
Edit: After the question has been clarified, I think Awesomium would be a good fit for your needs.
You can achieve the same functionality by embedding WebKit (or Gecko) but as far as I know that is exactly what Awesomium does behind the scenes.
An alternative is librocket—a C++ interface middleware package designed for game applications. As you can guess from the description it is a good fit for games or real-time applications.