Happy 1000th, Wingnut
My experience is that such flights are credited as BD ex-LHR (with bmi staff checking you in) and LH ex-FRA (with LH staff checking you in). Consistent, eh?
On the upside, I've managed to have discount LH tickets on BD metal awarded with full miles a number of times now. You need to write in, though, as arguing on the phone just irritates and confuses the DC operators.