I don't know. Wikipedia says:

According to the U.S. Food and Drug Administration, "Ibuprofen can interfere with the antiplatelet effect of low-dose aspirin (81 mg per day), potentially rendering aspirin less effective when used for cardioprotection and stroke prevention." Allowing sufficient time between doses of ibuprofen and immediate release aspirin can avoid this problem. The recommended elapsed time between a 400 mg dose of ibuprofen and a dose of aspirin depends on which is taken first. It would be 30 minutes or more for ibuprofen taken after immediate release aspirin, and 8 hours or more for ibuprofen taken before immediate release aspirin. However, this timing cannot be recommended for enteric-coated aspirin. But, if ibuprofen is taken only occasionally without the recommended timing, the reduction of the cardioprotection and stroke prevention of a daily aspirin regimen is minimal.[19]

Which of course doesn't mention the cancer effects, but there you go.

My intuition suggests that regular low-dose aspirin and weekly ibuprofen still has benefits that outweigh the risks, as compared to weekly ibuprofen only. However, my intuition didn't expect the effect, mentioned in the study's full text, where alternate-day low-dose aspirin appeared to have no effect on cancer.