We study the injection locking bistability of a specially engineered two-color semiconductor Fabry-Perot laser. Oscillation in the uninjected primary mode leads to a bistability of single mode and two-color equilibria. With pulsed modulation of the injected power we demonstrate an all-optical memory element based on this bistability, where the uninjected primary mode is switched with 35 dB intensity contrast. Using experimental and theoretical analysis, we describe the associated bifurcation structure, which is not found in single mode systems with optical injection.