Can I get a transit visa for each time through Beijing?

Hello,
I will be flying from Taiwan to Beijing on June 29 arriving at 16:25 and leaving the next day at 09:00 to fly to NYC. I would like to visit a friends house for the night. I plan on going to my friends house on the return on August 8 arriving at 14:20 from NYC and leaving the next day at 08:35 heading to Taiwan. So I would be spending a night each time at a friends house in Beijing. Is that okay under the 72 hour transit visa? I have an American passport and will be traveling with my Taiwanese wife. Also, is a full page required for the 72 hour transit visa? Thanks