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We investigated binary lenses with <inline-formula><math display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><msup><mi>r</mi><mi>n</mi></msup></mrow></semantics></math></inline-formula> potentials in the asymmetric case with two lenses with different indexes <i>n</i> and <i>m</i>. These kinds of potentials have been widely used in several contexts, ranging from galaxies with halos described by different power laws to lensing by wormholes or exotic matter. In this paper, we present a complete atlas of critical curves and caustics for mixed binaries, starting from the equal-strength case, and then exploring unequal-strength systems. We also calculate the transitions between all different topology regimes. Finally we find some useful analytic approximations for the wide binary case and for the extreme unequal-strength case.