like for Summer Camp absolutely.

What kind of paperwork?

I think it would depend on what kind of paperwork it is. I'd feel different saying they live there on a library card application than I would on a Medicaid application, for instance.

Also, you say the boys are with you most days.  Are they also with you at night, or are they at your house during the day and they go home to BM at night?

My experience is legal-wise doesn't have to jive with reality- skids might spend every day with you but if CO says BM has custody then that's usually their 'legal address' for anything official like school registration etc...

For smaller things like library or summer activities sign ups it might not matter...

Even when the family services placed SS with us full time we couldn't switch his address for school until the CO was also changed... I spent sooooo many hours driving him every day for months! Seriously it was 4 hours every school day!!!!!!!

Does your husband have a court order? 

If not, I would say there really isn't a right or wrong address but if there is, it would have to go by the custodial agreement. 

Unless, like another poster said it was for summer camp or something short term for contact purposes. 

It varies state by state but the courts often use overnights/where the child sleeps as where they "live." I'm not sure why you have them most days and your husband isn't the custodial parent, but it sounds like maybe things on paper don't fit with the reality of things. Not sure if that is the problem. I would say that if it involves anything where you or DH receive money (food stamps, etc.), you shouldn't put them as living with you or you may get in trouble. If you are providing most of their care, though, maybe having the custody agreement reflect that is the answer.