The strong absorption of liquid water in the infrared (IR) molecular fingerprint region constitutes a challenge for applications of vibrational spectroscopy in chemistry, biology, and medicine. While high-power IR laser sources enable the penetration of ever thicker aqueous samples, thereby mitigating the detrimental effects of strong attenuation on detection sensitivity, a basic advantage of heterodyne-measurement-based methods has-to the best of our knowledge-not been harnessed in broadband IR measurements to date. Here, employing field-resolved spectroscopy (FRS), we demonstrate in theory and experiment fundamental advantages of techniques whose signal-to-noise ratio (SNR) scales linearly with the electric field over those whose SNR scales linearly with radiation intensity, including conventional Fourier-transform infrared (FTIR) and direct absorption spectroscopy. Field-scaling brings about two major improvements. First, it squares the measurement dynamic range. Second, we show that the optimum interaction length with samples for SNR-maximized measurements is twice the value usually considered to be optimum for FTIR devices. In order to take full advantage of these properties, the measurement must not be significantly affected by technical noise, such as intensity fluctuations, which are common for high-power sources. Recently, it has been shown that subcycle, nonlinear gating of the molecular fingerprint signal renders FRS robust against intensity noise. Here, we quantitatively demonstrate this advantage of FRS for thick aqueous samples. We report sub-ìg/mL detection sensitivities for transmission path lengths up to 80 ìm and a limit of detection in the lower ìg/mL range for transmission paths as long as 200 ìm.