Does anyone here know why a codeshared NW flight with DL doesn't show up on Delta's site.

I have a voucher from Delta I want to use and fly out of DTW so of course NW has a lot more flights to different cities. I also have lot more skymiles and whenever I fly NW I always get skymiles instead of world perk miles.

EVERYTIME I go on delta's site for trips I take on NW the flights don't show up and I have even called Delta and was told the flights weren't ones they could book, yet on the last two trips I tried it on I took with NW when I got to the airport on the board it was showing a DL codeshare number.

How do you manage to book a NW as a codshare on delta? I would rather book through DL if the price is the same anyway since I get the 1000 bonus miles for booking online with DL that I lose if I book through NW in addiiton to the double am ex skymiles from delta.com