We present experimental and theoretical results for the phase behavior of mixtures of oppositely charged globular protein molecules in aqueous solutions containing monovalent salt. These colloidal mixtures are interesting model systems, on the one hand for electrolyte solutions ("colloidal ionic liquids"), and on the other for mixtures of oppositely charged (bio)macromolecules, colloids, micelles, etc., with the range of the electrostatic interactions (Debye length) easily tunable from much smaller to much larger than the particle size, simply by adding different amounts of monovalent salt. In this paper we investigate the phase behavior of such mixtures in the case that equally sized colloids have a large difference in charge magnitude. This is possible at any mixing ratio because small ions compensate any colloidal charge asymmetry. Our experimental system is based on lysozyme, a positively charged "hard" globular protein molecule, and succinylated lysozyme, a chemical modification of lysozyme which is negatively charged. By changing the solution pH we can adjust the ratio of charge between the two molecules. To describe phase separation into a dilute phase and a dense "complex" phase, a thermodynamic model is set up in which we combine the Carnahan-Starling-van der Waals equation of state with a heterogeneous Poisson-Boltzmann cell model and include the possibility that protein molecules adjust their charge when they move from one phase to the other (charge regulation). The theory uses the nonelectrostatic attraction strength as the only adjustable parameter and reasonably well reproduces the data in that complexation is only possible at intermediate , not too asymmetric mixing ratios, and low enough ionic strength and temperature.