While mixing with headphones is a bonehead idea if you can use monitors, do it anyway if you have to! The key phrase "if you have to".
I would move out of that apartment before I'd mix with cans personally, but you do what you gotta do, and work with what you have!
For those who say "don't use them" and offer no more advice, well they ARE right, but until they mail you a check for that first month's rent in your new HOUSE, check out the cans mentioned and take your pick.
I've HAD to mix with phones before, and while it IS a big pain in the ass, you can learn to compensate (to a point) for the "lying" they will do. A/B your mixes on a bunch of systems obviously, and do the best you can. And be prepared do remix, remix, remix....
Do you have a stereo in your house? If so, how loud is too loud? Mixing at softer levels was good advice........