It may be possible to do so, but I need to find out some more information in order to tell you most accurately.
1. Do you work?
2. What is your adjusted gross income for the year?
3. Can you be claimed on anyone elses return?
He could not claim the children because the children are you qualifiying children.
If you had earned less than 3500, he could have claimed you.
But in this case you nor your children are able to be claimed by your boyfriend.
Please see the example girl friend's child in publication 501 page 9. http://www.irs.gov/pub/irs-pdf/p501.pdf