Sorry, I thought I had given details enough.
We fly with Lufthansa Cph - Frankfurt and also Frankfurt - Mexico City. Herafter we change to InterJet to fly the last part to Cancun. It is this part that we hope to skip.
On our return flights (7 weeks later) we fly from Cancun - Chicago with United Airlines and hereafter Lufthansa the rest of the way (with a stop in Frankfurt).
On the documents given from the online agency it is all booked under the same booking number.

What we don't understand is, what if we actually missed a flight for some reason. You know, hypothetically if we fell asleep in the airport or something - would this also result in all our return flights being cancelled?

Kind regards Rasmus