Individuals exhibit a physiological and psychological response known as the stress coping response when they are exposed to external stimuli. This response represents a patterned reaction to stimuli and can be identified through fluctuations in hemodynamic parameters such as heart rate. The stress coping response is widely studied in physiological psychology, including evaluations of task-related concentration, and is expected to have practical applications in daily life. However, existing methods for measuring hemodynamic parameters typically require attaching devices to the fingers, which poses challenges for routine use due to physical constraints. Therefore, we focused on facial thermal images (FTIs) and facial near-infrared (FNI) images, which can be measured remotely using infrared thermography and near-infrared cameras, respectively. Fluctuations in skin blood flow due to changes in hemodynamic parameters are reflected in FTIs and FNIs. However, it remains unclear what specific characteristics appear in these multispectral facial images during such fluctuations. The purpose of this study was to investigate the characteristics of multispectral facial images and to evaluate response delays during fluctuations in hemodynamic parameters. We conducted stress coping response elicitation experiments and performed cross-correlation analysis between the acquired multispectral facial images and hemodynamic parameters. In typical subjects under passive coping responses, hemodynamic parameters and FTI showed a 17-second delay, with a negative correlation of approximately −0.5 in the nasal region and a positive correlation of approximately 0.64 in the cheek region. However, when averaging the correlations and time delays across all subjects under active coping responses, both FTI and FNI showed correlation values ranging from −0.10 to 0.09, indicating no significant correlation. Under passive coping responses, the correlation was weak, ranging from −0.20 to 0.14. This suggests that individual differences caused the values to offset one another when averaged. Regarding the delay, differences in wavelength were confirmed. For FNI, a delay of approximately 14 to 20 seconds was observed across the entire face under passive coping responses, while a delay of approximately 17 to 23 seconds was observed across the entire face under active coping responses. For FTI, delays in specific areas such as the nose and eye sockets were relatively short, at 1.75-4.81 seconds, while the rest of the face showed delays of approximately 15.38-37.06 seconds, indicating regional differences in delay. For FNI, no significant differences were observed in specific areas; a delay of approximately 14-23 seconds was found across the entire face. Differences in correlation and delay were dependent on the response and wavelength. Individual differences were confirmed. These results indicate that future remote measurements using facial images should select data considering wavelength properties and individual variability in correlation and delay.