ASP.Net uses the .Net platform and it produces web pages. C++ produces unmanaged executables and libraries. They are 2 different languages for 2 different things. You can still learn both at the same time, though.
Note however, that ASP.Net is a specialized use of .Net, so you should learn .Net first. To learn .Net you need to decide on a managed language. I recommend C#. I don't recommend C++/CLI because it will mess your head if you are learning C++ (unmanaged) too.