Well that at least is something as if it is dodgy and his bank account gets shut down you may emerge unscathed.
Titchy is absolutely right, though, this is immediate contact with the bank and potentially, the police.
At best, he is ridiculously naive.
Middle ground, he is as financially irresponsible as his family.
At worst, he knew full well and is engaging in criminal activity.
I suspect it's either of the first two options but I'd be insisting that you are involved in the "clearing up" (ie, speaking to both bank and police) to protect yourself, let alone him.
Sadly, this is going to result in huge fallout between the family I suspect. Because your SIL is going to have some questions to answer too.
I would also be insisting that YOU take over any joint finances in future, even though this was his personal money.