Well the reality is that most people listen to music on headphones, earbuds or something along the lines of that.
I try to keep myself 50% headphones and 50% studio monitors. There are times when I work during the night a lot which means I'm only working with headphones. This way volume levels stay the same and I get less ear fatigue etc. To be honest I suggest people to invest in proper headphones. I think the Beyerdynamic DT880 headphones I own are extremely good for making even serious mixes. Obviously most of my work gets done with my monitors but I always check things with my headphones.
In the end it's all about getting to know your monitoring gear and trusting it. I think in this case the problem was that you're simply so used to having monitors instead of headphones rather than the headphones being bad.