We consider the problem of estimating unknown transmittance θ of a target bathed in thermal background light. As quantum estimation theory yields the fundamental limits, we employ the lossy thermal-noise bosonic channel model, which describes sensor-target interaction quantum mechanically in many practical active-illumination systems (e.g., using emissions at optical, microwave, or radio frequencies). We prove that quantum illumination using two-mode squeezed vacuum (TMSV) states is asymptotically optimal in the limit of low transmitted power and high number of probes. We characterize the optimal receiver structure for TMSV input, and show its advantage over other receivers using both analysis and Monte Carlo simulation. In conclusion, we discuss implications of our results, possible experimental evaluation, application to covert or low probability of detection/intercept (LPD/LPI) transmittance sensing, and other recent developments.