Since member discount nights come from the points pool of room, they are treated as member stays with regards to housekeeping. They will combine your points & cash reservations for the housekeeping schedule.
Last year I booked Friday & Saturday nights as member cash, then Sunday to Thursday as points. They scheduled my trash & towel for Monday, day 4 of the combined stay. I also got keys & parking pass for the entire stay, I did not have to go back to the front desk on Sunday to get new ones like you would with a CRO stay.
This year I booked Sunday to Thursday nights on points and Friday on an AP rate through CRO. We did get full housekeeping on Friday but I had to go to the front desk to get new keys & parking pass on Friday morning. Luckily we did not have to change rooms.