Knowledge of flame responses to acoustic perturbations is of utmost importance to predict thermoacoustic instabilities in gas turbine combustors. However, measuring transfer functions linking acoustic quantities upstream and downstream of flames are very challenging in practical systems and these measurements can significantly deviate from state-of-the-art models. Moreover, there is a lack of studies investigating the effect of hydrogen enrichment on the response of natural gas (NG) flames. In this work, measurements of flame transfer matrices (FTMs) of turbulent H2/NG flames in an atmospheric combustor featuring an axial swirler burner have been performed, allowing us to unravel the transition between FTM in fully premixed (FP) and in technically premixed (TP) conditions. Furthermore, imaging of OH* chemiluminescence and OH-planar laser induced fluorescence are obtained for characterizing the topology of the flame for varying H2 fraction and mixing conditions. Transfer matrices are measured using the multimicrophone method for H2 fractions ranging from 12% to 43% in power. Afterward, the flame transfer functions (FTFs), which linearly relate the coherent fluctuations of the heat release rate to the acoustic velocity oscillations, are obtained from the FTM by using the Rankine–Hugoniot jump conditions across the flame. Using the OH* chemiluminescence intensity as a surrogate for the heat release rate, the FTF based on this optical measurement is also extracted and compared to the one exclusively obtained with the multimicrophone method. As expected, the two different methods are in very good agreement for the FP case and significantly differ for the TP case. Indeed, chemiluminescence fluctuations cannot be directly linked to heat release rate fluctuations when the acoustic forcing induces equivalence ratio fluctuations at the flame, making the optical method unusable for TP configurations. We also show that the two methods agree in the high end of the explored excitation frequency range and we provide an explanation to this intriguing finding. Moreover, we investigate the sensitivity of the FTM measurement to the estimate of the speed of sound in the rig in FP conditions. Finally, the measured FTFs are fitted with FTF models based on multiple distributed time delays. This allows us to explain the frequency dependence and the hydrogen fraction dependence of the gain and the phase in FP and TP conditions.