144H visa for European citizenships

Hello,

Me and my boy friend is planning to travel to Hanoi, vietnam in August through Beijing. So, what if we flight from Helsinki to Beijing and staying there for 5 days then fly from Beijing to Hanoi. Do I need to fly with same airline or can be different ones?

The route will probably be Helsinki - Beijing 16/8 and 22/8 Beijing to Hanoi. Are we eligible for the 144-hour free travel?

Thank you in advance :)