bmibaby may be using bmi aircraft in Manchester at the moment, but the reservations, cabin crew and onboard service are all bmibaby. It is no different to any other airline that subs in aircraft from another carrier. bmibaby and bmi co exist in Manchester very well as different airlines, each run in very different ways that suit their operational requirements
The idea that bmi and bmibaby should be merged in order to reduce costs is ridiculous as bmibaby's operating costs are much lower than bmi's with completely different operational structures, labour contracts, business models etc... that suit both airline's positions in their respective markets.