Europe to Beijing, 2 days in Beijing, then flight to Japan, back to Beijing for less than 24 hours

Hello,
we are a family of Americans and Russian nationals, PR in Switzerland. We are flying to Beijing, staying there in a hotel and leaving 70 hours later to Osaka in Japan (tickets confirmed). After spending 10 days in Japan we are flying back to Beijing in the evening and flying out early morning next day back to Europe. Do I understand correctly that we can count on 72 hours visa on one direction and 24 hours direct transit with temporary stay permit on our way back? The airlines we are flying in Beijing from Europe and flying to Japan are different.