1-stop trip booked as separate trips; how to check bags?

I recently booked the following flights with a Delta phone agent:

Outbound: 1/6 CID->DTW->PEK, Layover in DTW is 4 hr 49 min.
Returning: 4/15 PVG->DTW->CID, Layover in DTW is 1 hr 30 min.


However, on Delta's iPhone App, it shows I have three (3) trips under the same reservation:
1. 1/6 CID-DTW, non-stop;
2. 1/6 DTW-PEK, non-stop;
3. 4/15 PVG-CID, 1-stop.
It is as if the CID-DTW-PEK trip is separated into two trips.

On Delta.com, all four segments are separately listed. However, while it shows "Layover in Detroit-Wayne County, MI 1H30M" for the returning trip, there is no such sentence for the outbound trip.

With these evidence, I am wondering if my 1-stop outbound trip was actually booked as two separate trips. If so, at CID, am I still able to check all my bags under the international flight allowance and have them go all the way to PEK?

I called Delta earlier. Although I received assurance that my flights and bags will be processed correctly, I am not sure if they understood the problem or considered it as a problem at all.

Any previous experience on similar situations?

Thanks!