How to determine the transfer function of a system including disturbances
It is the purpose of such a (complicated) feedback arrangement to process the input signal in a certain manner ("Follower" control, mostly specified in the time domain) as well as to reject any disturbances as much as possible. 

This leads to TWO different transfer functions which govern the design of the whole system: (a) Signal Transfer Function (disturbances Vd=0) Hs(s)=Vout(s)/Vin(s)  and (b) Disturbance Transfer Function (Vin=0) Vout(s)/Vd(s) (corrected).

That means: You cannot define a transfer function that considers both inputs (signal and disturbance) at the same time.

Comment 1: In your first sentence you speak about the "open-loop" transfer function. Don`t forget that - finally - it is the closed-loop transfer functions that matters for both cases.

Comment 2: Of course, you can determine the combined output signal in presence of both sigbnal and disturbance.