Can my husband offer to buy me off re: custody/visitation of my children? Is this legal?

Ask him to put it in writing.  Once he does that, if he's that stupid, take the document to court, on a motion to enforce your back support, and ask the judge to put him in jail for contempt until he pays you the $11,000 he's saying he has, against those arrears (which I'm assuming are $40,000 or so, not $40.00-ish).

File the motion, and tell the court about the offer, even if he isn't stupid enough to give you evidence like something in writing, or a voicemail message that you can save and replay.

Even if you signed something like this, it probably wouldn't be enforceable, because most courts don't give you the right to give up child support:  it doesn't belong to you, it belongs to the children.  Even a court itself does not have the power to remove child support arrears, in most cases.