When a Ne:HBr or a Ne:HI sample is codeposited at approximately 5 K with discharge-excited neon atoms, the infrared spectrum of the resulting solid includes not only the absorptions of the HX molecule and its multimers but also a prominent absorption of HBr+ or HI+. The absorption of each of the two cations lies within a few cm(-1) of its gas-phase band center. The vibrational fundamentals of DBr+ and DI+ are also identified in experiments on deuterium-enriched samples. Other infrared absorptions are assigned to normal and deuterium-substituted (HBr)(2)(+) and (HI)(2)(+), as well as to BrHBr-, BrDBr-, and IHI-. Studies of changes in the absorption spectrum following exposure of the deposit to filtered visible and near ultraviolet radiation support these assignments and provide further information on photodissociation and photodetachment processes occurring in these systems.