I need a little bit help see if this breaks delta's rules?

I'm booking

Friday night departure: DL JFK-LHR
AND
Next Friday returning DL LHR-JFK together as round trip.

The JFK-LHR flight gets me into london on Saturday morning. I will stay in London for one day and then take the following flight:
AF LHR-CDG-SGN
AND
return to LHR on AF next thursday.

Then I will have one day layover in london and I will take DL LHR-JFK back. If i put down my skymlie number for both DL and AF ticket, would that be a problem? Is that a back to back ticketing? Or back to back ticketing only refers to tickets on the same airline?