Different Airlines, each one ticket - Transit visa still possible?

Can I book a flight Frankfurt-Beijing-Frankfurt with one Airline (e.g. Lufthansa), three weeks between arrival in/departure from Beijing, and another flight Beijing-Bangkok with another Airline (e.g. Hainan) within those three weeks and then get 72 hrs free transit for both stops in Beijing?
Or is transit visa only possble if the ticket is from the same Airline?