Schroeder-phase harmonic tone complexes have a flat temporal envelope and either rising or falling instantaneous frequency sweeps within F0 periods, depending on the polarity of the phase-scaling parameter C. Human thresholds for detection of a pure-tone target added to a Schroeder HTC can be 10-15 dB lower for the positive Schroeder (downward-sweeping) compared to negative (upward-sweeping), potentially due to the impulse response of the basilar membrane though this hypothesis remains controversial. Specifically, the upward-gliding impulse response observed empirically in several studies is expected to produce a peakier envelope response for positive Schroeder HTCs, thereby reducing masking compared to negative Schroeder HTCs. Birds provide an interesting animal model for studying Schroeder masking because prior studies suggest less behavioral threshold difference between Schroeder maskers of opposite polarity. However, neurophysiological mechanisms have not been explored and previous behavioral studies mostly used Schroeder HTCs with relatively low F0s. To gain further insight into underlying Schroeder masking mechanisms, we performed operant-conditioning experiments in budgerigars (Melopsittacus undulatus), a parakeet species, using a wide range of F0 and C values. Awake neurophysiological recordings in the avian inferior colliculus, a major envelope processing station in the midbrain, characterized neural encoding of behavioral test stimuli. Behavioral Schroeder masking thresholds increased with increasing F0 and showed minimal difference between opposite Schroeder polarities for all conditions, similar to prior studies in this and other bird species. Neural recordings showed prominent temporal and average-rate-based encoding of Schroeder F0, and in many neurons, marked response asymmetries between opposite Schroeder polarities. While response bias varied considerably across neurons, average bias of the population shifted from negative to positive with increasing characteristic frequency, with a breakpoint at ~2-3 kHz. Response bias was weakly associated with lower Schroeder-masked tone detection of neurons for the 400-Hz F0 only. These results challenge the common assumption that a peakier masker response results in a lower threshold for target tone detection with this paradigm.