The passive applies as though auxiliaries were not present, and then any auxiliaries take part in subject-auxiliary inversion just as they would in an active sentence. This is one of the arguments for deriving auxiliaries from outside the core part of a sentence (by a version of Subject Raising).
So, without passive, we have
- will [ someone offer courses ]
- someone will offer courses (by Subject-Raising)
- will someone offer courses? (by Subject-Aux Inversion)
And with passive, we have
- will [ someone offer courses ]
- will [ courses be offered by someone ] (by Passive applying to lower clause)
- courses will be offered by someone (by Subject-Raising)
- will courses be offered by someone? (by Subject-Aux Inversion)
Examples with more complicated sets of auxiliaries work the same: "Courses should have been being offered" = "Someone should have been offering courses".
This is an outline of the treatment in McCawley's TSPE.