First, a minor correction: The North Shore Line was the Chicago North Shore & Milwaukee Railroad, or CNS&M, not the "CM&NS."
Orangeline is correct in that Samuel Insull controlled the "big three" Chicago interurbans, the elevated system and the electric utilities in the 1910's and 1920's, and it was his influence which allowed the North Shore and the CA&E to operate over the 'L.'
The North Shore entered the elevated system over tracks now used by CTA Purple and Yellow line trains in Wilmette, Evanston and Skokie, while the "Roarin' Elgin" operated over the Garfield elevated route, which was replaced by the present-day Congress line (the Forest Park branch of the Blue Line) about the time the CA&E ended operation. Until 1951, rapid transit trains and CA&E interurbans shared the tracks as far west as Bellwood Avenue, where the CA&E continued west to Wheaton and rapid transit trains on the Westchester route turned south onto a private right-of-way to the terminal at 22nd and Mannheim.
The North Shore and the CA&E were considered interurbans rather than rapid transit lines. It's difficult to even imagine the kind of operation that existed "back then" today, for a variety of reasons -- traffic today would likely require the interurbans to use standard railroad-size equipment, like NICTD operates, which would make operation on the 'L' impossible; if smaller equipment were used the FRA would likely not allow freight operation on the same railroad; and modern signals and ATC on the elevated have greatly reduced its capacity for trains, so it's unlikely the CTA could handle the additional traffic. Also remember the CTA was itching to get rid of the interurbans back in the '50s -- even then, all those extra trains were a hassle the CTA was quite content to do without.
Sorry if I've rambled here, but hopefully I've shed a little more light onto the topic.