This is incompletey incorrect.

They're both IATA airlines, so you're 100% protected under IATA resolution 735d, INVOLUNTARY CHANGE OF CARRIER, ROUTING, CLASS OR TYPE OF FARE, also known as PSC(30)735d (for the 30th Passenger Services Conference). These rule apply irrespective of the number of tickets involved and are binding on all IATA signatories.

However, since you're on separate itineraries, at check-in, present proof of continuing voyage and insist that it is entered into your reservation; this will let ground personnel at ORD know of your connection and will facilitate their working on your reaccommodation before you get there in case you're delayed.