Are we eligible for 144-hour free transit visa Beijing?

Hi there.
My husband and I are travelling to Beijing from Frankfurt, Germany. On our way to Melbourne, Australia we will stay in Beijing from Fri. 27 Apr. to Wed. 2 May. (We will then return to Frankfurt later in May, from Australia via Beijing but will not exit the airport).
I am an Australian citizen - my husband is a German citizen.
Do we qualify for the 144hr free transit visa in Beijing?
Do we need another visa for our transit through the airport on the way back home to Frakfurt?

(We've called the Chinese consulate in our local city and they have been very uninformed and not helpful... I feel they just want us to pay the money and purchase standard tourist visas :-( )

Thanks so much.