Psychology Today has a search function that lets you filter by insurance. The last time I looked this groups was one of the few meeting your criteria. They took BC/BS then, but things can change of course:
http://www.dandelionpsychotherapy.com/children-and-families

I suggest you sit down with your computer and go through all the mental health providers listed. I did this one afternoon with two laptops--on one I went through the insurance lists and on the other I googled practitioners' names. I probably spent three hours doing this before I got a short list of two to make contact with. We are now seeing one of them who hits all your requirements. It is possible to find someone but it takes time and the person you end up with will be likely be someone with no reputation (it doesn't always matter) and probably an LCSW.

I have an Aspergers/ADHD son with depression and anxiety. It has been recognized by a therapist that saw him individually that we would be better served wtih parent/family play therapy. Anyone know anyone in NW DC or nearby MD that provides such therapy and takes insurance? Best situation would be weekend hours.