It's perfectly possible to mix great sounding music on headphones. But you need a pair of good quality headphones that have as little color as possible - I have a pair of ATH-M50's and they're fantastic for mixing.
But what makes all the difference is if you mix through a speaker simulator like the Focusrite VRM Box. They recreate the tonal characteristics of various studio monitors and home speakers (e.g. laptop, desktop, TV, home hi-fi etc) so that you can hear how your mix is going to sound on a variety of systems. What they don't do is fully recreate the experience of listening on speakers, but they do offer a diversity of sonic perspectives to check your mix against. If it sounds good on every simulation on the VRM Box, there's a very good chance it's going to translate well to a variety of real world speakers as well. Probably one of the most useful purchases I ever made. But you have to pair them with a good quality pair of cans.