Bmi baby ltd, british midland airways ltd and british midland regional ltd all trading as different companies but under the ownership of LHBD Holdings ltd. LHBD is in tern owned by Lufthansa AG. Pilots of the individual ltd companies have no greater ability to lay claim that they work for bmi (group) as they would Lufthansa. A bit like working for British gas or centrica.
Thats all fine and dandy, but if their contracts state they work for the parent company, I'd say things are a little trickier.