I have had problems with my ILs for the past 11 years. To the point where my MIL tried to set my BF up with someone else to get him to dump me!! And the lies she told were horrendous!
He could see it was hurting me, but tried to ignore it in the hope it would all go away. Well, it didn't, but I persevered and this year I gave her enough rope to hang herself! After our son was born, she stopped talking to us because we stopped dancing to her tune, and after about 3 months of nasty emails she told him a whopping lie about her health, so that they could start talking without her apologising for her behaviour!
So, the upshot is, we started talking to her again, and when her lies were found out we confronted her. Now my man stands by me. and we visit because of our son. However, things are much better between us all now!!
My advice to you would be, rise above it. Don't give your BF the opportunity to lay blame at your door, and eventually they will go too far, and your BF might start seeing things for how they really are from your perspective. Keep going round, smile, and do your utmost to be perfectly pleasant!!
Good luck!! Hope it gets better for you!!
ERx