Individuals with sensorineural hearing loss may have similar monaural thresholds (i.e., pure tone audiogram) but perform quite differently on tests of speech-in-noise. Additional testing using complex, binaural signals may be able to differentiate individuals with similar pure-tone hearing. Here, individuals with mild-to-moderate hearing losses were evaluated using tests of spectral, temporal, and spectrotemporal modulation, diotic and dichotic frequency modulation, gap detection, 2 kHz tone-in-noise, and spatial release from masking. Binaural psychoacoustic measurements were evaluated on an iPad using the Portable Automated Rapid Test (PART) app. Normal hearing listeners were evaluated as controls. Normal hearing results were similar to normative data previously collected by Lelo de Larrea-Mancera and colleagues (2020) and hearing-impaired results were elevated for most binaural measurements evaluated compared to normal hearing controls. Binaural psychoacoustic data were successfully measured for individuals with mild-to-moderate amounts of hearing loss using a portable system. Results show that evaluating complex stimuli on clinical populations using a portable device is feasible. Additionally, if accomplished on a larger scale the current test battery may likely add useful information on how hearing-impaired listeners process complex binaural stimuli and could compliment current clinical diagnostic test battery and, potentially, guide hearing aid fittings.