Hi Laur and welcome.
Have you read around the forums a bit? Probably the most important thing is learning as much as you can about alcoholism. Not for your Husband, for yourself, to help give you peace of mind.
It's hurtful, yes, that his family has been lied to and they believe him and blame you, but as with this whole thing, you have no control over him and certainly no control over them.
You say you know you need to leave, does that mean that is your plan? If so, have you actually got a plan?