Every-day acoustical environments are often complex, typically comprising one attended target sound in the presence of interfering sounds (e.g., disturbing conversations) and reverberation. Here we assessed binaural detection thresholds and (supra-threshold) binaural audio quality ratings of four distortions types: spectral ripples, non-linear saturation, intensity and spatial modifications applied to speech, guitar, and noise targets in such complex acoustic environments (CAEs). The target and (up to) two masker sounds were either co-located as if contained in a common audio stream, or were spatially separated as if originating from different sound sources. The amount of reverberation was systematically varied. Masker and reverberation had a significant effect on the distortion-detection thresholds of speech signals. Quality ratings were affected by reverberation, whereas the effect of maskers depended on the distortion. The results suggest that detection thresholds and quality ratings for distorted speech in anechoic conditions are also valid for rooms with mild reverberation, but not for moderate reverberation. Furthermore, for spectral ripples, a significant relationship between the listeners’ individual detection thresholds and quality ratings was found. The current results provide baseline data for detection thresholds and audio quality ratings of different distortions of a target sound in CAEs, supporting the future development of binaural auditory models.