We propose simultaneous αβ decay as a novel mode of nuclear instability that involves the strong and weak interactions in a single quantum transition. We develop a theoretical framework to predict its branching ratios and α-energy spectra, establishing exclusive and inclusive criteria based on whether the individual α and β channels are closed or open. A global survey of the nuclear chart identifies five exclusive αβ− candidates, all predicted to be experimentally inaccessible, and ranks the leading inclusive candidates for both the αβ− and αβ+ modes. Remarkably, six of the top αβ+ candidates coincide with known β-delayed-α precursors. The observed α spectra are naturally accounted for by simultaneous αβ+ emission without additional assumptions, indicating a substantial and possibly dominant direct component. Our findings establish simultaneous αβ decay as a distinct radioactive process and a sensitive probe of the interplay between the strong and weak interactions.