Am I eligible for 144-hour Visa-Free Transit

I'm looking for tickets to visit Ulaanbatar with a 5 day layover in Beijing. Is the following trip eligible for a 144-hour Visa-Free Transit on our outward journey and the 24-hour Visa-Free Transit on our return trip?

- Tickets Amsterdam - Beijing (roundtrip August 1st - August 15th)
- Tickets Beijing - Ulaanbatar (roundtrip August 5th - August 15 th)

As I see it, we will qualify because we arrive in Beijing (coming from Amsterdam) and leave to a third country (Ulaanbatar). Does it matter that we have roundtrip tickets?

Also we will arrive at Beijing Daxing and leave at Beijing Capital (vice versa at the 15th).