Rationale The nature and predictors of insensitivity to aversive consequences of heroin + cocaine polysubstance use are not well characterized. Objectives Translational methods incorporating a tightly controlled animal model of drug self-administration and measures of inhibitory control and avoidance behavior might be helpful for clarifying this issue. Methods The key approach for distinguishing potential contributions of pre-existing inhibitory control deficits vs. drug use history in meditating insensitivity to aversive consequences was comparison of two rat strains: Wistar (WIS/Crl), an outbred strain, and the spontaneously hypertensive rat (SHR/NCrl), an inbred strain shown previously to exhibit heightened cocaine and heroin self-administration and poor inhibitory control relative to WIS/Crl. Results In separate tasks, SHR/NCrl displayed greater impulsive action and compulsive-like behavior than WIS/Crl prior to drug exposure. Under two different schedules of drug delivery, SHR/NCrl self-administered more cocaine than WIS/Crl, but self-administered a similar amount of heroin + cocaine as WIS/Crl. When half the session cycles were punished by random foot shock, SHR/NCrl initially were less sensitive to punishment than WIS/Crl when self-administering cocaine, but were similarly insensitive to punishment when self-administering heroin + cocaine. Based on correlation analyses, only trait impulsivity predicted avoidance capacity in rats self-administering cocaine and receiving yoked-saline. In contrast, only amount of drug use predicted avoidance capacity in rats self-administering heroin + cocaine. Additionally, baseline drug seeking and taking predicted punishment insensitivity in rats self-administering cocaine or heroin + cocaine. Conclusions Based on the findings revealed in this animal model, human laboratory research concerning the nature and predictors of insensitivity to aversive consequences in heroin and cocaine polysubstance vs. monosubstance users is warranted. Supplementary Information The online version contains supplementary material available at 10.1007/s00213-022-06134-4.