My girlfriend and her 2 children live with me, can we file jointly or can I claim them?

My girlfriend has 'sole' custody of both children. She does work; brings in approximately $9850 a year. I don't charge her rent, but I don't really pay anything more than I would if they did not live with me...just in food (which we share the cost of). She pays all of their individual (additional) expenses.
Can we file jointly, or am I able to claim her/them?