Measuring and analyzing both nonlinear-distortion and linear-reflection otoacoustic emissions (OAEs) combined creates what we have termed a "joint-OAE profile." Here, we test whether these two classes of emissions have different sensitivities to hearing loss and whether our joint-OAE profile can detect mild-moderate hearing loss better than conventional OAE protocols have. 2f1-f2 distortion-product OAEs and stimulus-frequency OAEs were evoked with rapidly sweeping tones in 300 normal and impaired ears. Metrics included OAE amplitude for fixed-level stimuli as well as slope and compression features derived from OAE input/output functions. Results show that mild-moderate hearing loss impacts distortion and reflection emissions differently. Clinical decision theory was applied using OAE metrics to classify all ears as either normal-hearing or hearing-impaired. Our best OAE classifiers achieved 90% or better hit rates (with false positive rates of 5%-10%) for mild hearing loss, across a nearly five-octave range. In summary, results suggest that distortion and reflection emissions have distinct sensitivities to hearing loss, which supports the use of a joint-OAE approach for diagnosis. Results also indicate that analyzing both reflection and distortion OAEs together to detect mild hearing loss produces outstanding accuracy across the frequency range, exceeding that achieved by conventional OAE protocols.