We report the first realization of a biomolecular AND gate function with double-sigmoid response (sigmoid in both inputs). Two enzyme biomarker inputs activate the gate output signal, which can then be used as indicating liver injury, but only when both of these inputs have elevated pathophysiological concentrations, effectively corresponding to logic-1 of the binary gate functioning. At lower, normal physiological concentrations, defined as logic-0 inputs, the liver-injury output levels are not obtained. High-quality gate functioning in handling of various sources of noise, on time scales of relevance to potential applications, is enabled by utilizing "filtering" effected by a simple added biocatalytic process. The resulting gate response is sigmoid in both inputs when proper system parameters are chosen, and the gate properties are theoretically analyzed within a model devised to evaluate its noise-handling properties.