what are his odds of getting joint custody?
I will assume the Divorce is taking place in Utah. A quick search of Utah Laws indicate that the court considers Best Interest of the Child, and other relevent factors.
In my opinion, based your factual statements' , a registered Sex Offender (and his specific circumstances) would probably be used agianst him to be awarded anything over "supervised visitation".
As another reply noted, the stigma attached with registered Sex Offender's, would also make it difficult for him to enjoy certain activities with his biological children.
If he truely wants to move on with his life, [presumably to be with you] he may just have to accept his current wife's conditions, and perhaps consider revisting the issue after a few years.
Here is a link to a website you might find helpful to this discussion: http://www.helpyourselfdivorce.com/utah-child-custody-laws.html
I'm not a lawyer. This is only my opinion /suggestion. Most Replys' are based on information provided by the "original post" (OP).