We analyze theoretically and experimentally cases of asymmetric detection, stimulation, and loss within a quantum nonlinear interferometer of entangled pairs. We show that the visibility of the SU(1,1) interference directly discerns between loss on the measured mode (signal) and the conjugated mode (idler). This asymmetry also affects the phase sensitivity of the interferometer, where coherent seeding is shown to mitigate losses that are suffered by the conjugated mode; therefore increasing the maximum threshold of loss that permits sub-shot-noise phase detection. Our findings can improve the performance of setups that rely on direct detection of entangled pairs, such as quantum interferometry and imaging with undetected photons.