How do I say: We welcome our new pastor James Quinn; his wife, Deana and their children John, Patti, and Chris. Is that the correct way to punctuate?
According to Wikipedia, In general, the comma shows that the words immediately before the comma are less closely or exclusively linked grammatically to those immediately after the comma than they might be otherwise. So you could just replace ';' with ',' and it would makes sense more and will be more consistent.
We welcome our new pastor James Quinn, his wife Deana, and their children John, Patti, and Chris.
You only need a semi colon if the list is more complicated
You can find an example here: http://www.grammar-monster.com/lessons/semicolons_in_lists.htm