As we have already reported, the couple long ago agreed to joint custody of their 3 kids. There are 2 elements to the agreement -- legal and physical custody.

Legal custody is simple ... they will jointly agree on decisions that affect the kids, such as education and various activities.

As for physical custody, that's where it gets tricky. As we reported, the divorce was held up for a long time because Ben was on and off the bottle, and Jennifer didn't want to strike any custody arrangement until he was sober and stable.

We're told the physical custody agreement is vague ... it doesn't outline any specific division of time with the kids. But, we're told, at least at the beginning, Jen will get the lion's share of custodial time, and when Ben has the kids he will have a monitor to ensure he's sober and the kids are safe.

There's another factor -- their kids are older now -- 12, 9 and 6 -- and they may be conscious of Ben's problem with alcohol and how it's affected their family, and they will have a voice as well.