In terms of both reservations systems and actual operations, United is still just an "Other Airline" in terms of a Continental itinerary, and vice-versa.

Just like any other airline which might have a flight on the itinerary, including competitors (which CO can book, as can any IATA airline.)

That means CO's reservation is the "Master PNR" and shows all flights operated by all carriers in the itinerary, including OALs (Other Airlines).

United is simply an OAL. Continental messaged to that OAL the segments relevant to the OAL, and that OAL (United) created their own PNR based on what the Master PNR airline sent them. Typically an OAL copy of an itinerary for which they aren't the master PNR/ticketing airline only includes their own flight, and the last flight before their own first flight in the itinerary. Sometimes it also shows the first flight on yet another airline (or the ticketing airline) following the last flight this particular OAL has in your itinerary.

Example:

CO ticket
CO Master PNR
Full Itinerary: SEA-IAH (CO) IAH-IAD (CO) IAD-LHR (UA) LHR-IAD (UA) IAD-EWR (CO) EWR-SEA (CO).

I would expect UA, as "just another OAL", only to have these segments at United.com and in United's own back-end reservation system:
IAH-IAD (CO) last flight before the first United flight
IAD-LHR
LHR-IAD
and nothing more. Maybe they would have IAD-EWR (CO) but not EWR-IAD.

They're not one airline. They're two different airlines owned by the same holding company, sharing a lot of the same branding and some of the same ground services. But they are still mostly separate, and the reservations system, along with the FAA operational certificate, are two of the biggest areas where they are still 100% different airlines.

In March, when they combine reservation systems, then it'll all show up on either site (or on the only remaining site).

IMHO you have absolutely nothing to worry about. You're understandably from the branding changes, going on the false assumption that they are the same airline. But if you're not comfortable with this, call.