We compare two nonlinear-optical techniques for measuring chirality of isotropic surfaces. One technique measures the difference in the efficiency of surface second-harmonic generation between the cases of left-hand and right-hand circularly polarized fundamental light and the other measures the difference in the efficiency between the cases of fundamental light linearly polarized -45 degrees and +45 degrees with respect to the p-polarized direction. A nonzero difference in either case indicates chirality, where no difference should be measured for an isotropic achiral surface. We examine the complementariness of these two techniques theoretically and experimentally. In experiments utilizing thin films of a chit-al poly(isocyanide), we measure the second-harmonic response as a function of the state of polarization of the fundamental light when manipulated by both quarter and half waveplates. We extract the circular and Linear differences from these more complete measurements and find the largest circular and linear differences to be 23% and 118%, respectively.