I'd say stick to C# ASP.NET for now.
Get really proficient with it, know it inside out.
It's better to be really good at one thing than to know a little bit about two things (of course it's even better to be really good at one thing and know a bit about something else too :)), so I recommend you stick to C# ASP.NET.
After that try some Node.js if you want.
Unless, of course, you need Node.js now for a job or something.
You'll find that it doesn't really matter if you use Node.js, C# ASP.NET, PHP or what have you.
You have a (REST) server listening for requests, handle them and send a response.
Whether you do that in C# ASP.NET or Node.js is actually irrelevant for your front-end, the user will never know.
In fact, as a C# ASP.NET MVC developer I was up and running with Node.js in a few hours (getting really proficient with it takes more time, of course)!
Sure, there are some differences between C# ASP.NET and Node.js (of course it's a different language, but there's also the whole web server which is single threaded in Node.js), but I tend to see them as details in the big picture. Both require knowledge of HTTP(S), JavaScript, JSON and HTML, especially when you do full stack.
Having said that, Node.js is not better than C# ASP.NET, it's simply different.
If you'd really like to start out with Node.js I can recommend my own blog series:
MEAN web development[
^].