North Ave. and Roosevelt Rd. go from the lake to about 2/3 of the way to Iowa. The names end at the DuPage/Kane county line, though. After that, they are just IL64 and IL38.
The numbering system for just about all Chicago roads ends at the Chicago city limits, except for some of the streets on the south side, which continue all the way down into Will County.
Even stranger is that there is a pocket of streets in Dyer Indiana that are numbered according to the Chicago system, as if they had expected the street grid to expand that far south and east. Expand to Hammond, Schererville, St John and you'll see east/west streets that are numbered in the 40s (the Gary Indiana scheme), then in the high 90s (Lake County Indiana scheme?), then the 210s (Chicago scheme), then the 70s (back to the Gary scheme).
EDIT - Chicago did a mass street renumbering (with a few street name changes too) in the early 20th century. It would be interesting to know if some of the suburban street numbering schemes for the roads that cross municipal boundaries are still using the old system and that is why the street numbers seem to reset once you exit the city.
