Metropolitan Jackson is actually divided between three state senators, one for Madison, one for Gibson, and one for Chester counties (I don’t know why, I can understand why for Nashville, which has 2.1 million population, but not for Jackson, I’d think for it they’d want to consolidate it into one state senator).
Jackson isn't split. The outlying areas aren't really part of the metro area.
I do consider Gibson and Chester part of Jackson, Gibson because of Milan, Humboldt, and Medina and Chester because of Henderson. Only the southern part of Gibson County (those three towns) is really suburbs of Jackson, although they are. US 45 BYP is six lanes north of I-40 and carries a large amount of traffic to Oil Well, it slows down slightly past Oil Well when you get past the restaurants and shopping but still a decent amount past there. If Milan, Humboldt, and Medina were not in Gibson county, I would not consider Gibson county part of the Jackson Metropolitan Area because Trenton and Bradford absolutely are not. I would be willing to say that Henderson and therefore Chester county is not part of the metropolitan area though, especially since they are so far removed from I-40, even though they are closer to downtown.
There is not a good way to get between the north side of Jackson and the south side of Jackson or vice-versa because you have to go through downtown, although Jackson has grown predominately north and very little south and east and none west. It can't grow west despite Interstate 40 because of swamp / wetlands. I do not consider the small towns 25 or 30 miles out of Jackson as part of the metropolitan area at all.