If the typical 70% rubbing alcohol isn't removing everything, try the higher concentrations (90%+ solution). The 70% solution works, but not quite as well as the higher concentrations. As a bonus, rubbing alcohol also removes permanent marker if someone should accidentally take one to your board or refrigerator instead of a dry erase marker.
Failing that, try peroxide. That works pretty well, too.
Here are a few suggestions I've tried, but DON'T recommend:
WD-40 It works but it smells. It's also a solvent and I've found it removed some of the smooth finish off my dry erase board (may not apply to your refrigerator), so the marker became hard to get off from then onward. And if you don't get all the WD-40 off, the markers won't write as well.
Hairspray used to work, but many hairsprays don't contain much, if any, alcohol anymore.
Toothpaste is an abrasive. It cleans a lot of things, but when you micro scratch the surface you are cleaning, it creates a matte surface that makes the marker really hard to get off the next time.
Optional Experiment: Once you get the blue stains off, try sealing the surface of your refrigerator with paste car wax. I've not tried it myself, but I've heard that makes the dry erase marker easier to wipe off to keep the surface clean. I've not tried this yet, but let me know if it works.