Recent studies have demonstrated that heart rate (HR) could be estimated using video data [e.g., exploring human facial regions of interest (ROIs)] under well-controlled conditions. However, in practice, the pulse signals may be contaminated by motions and illumination variations. In this paper, tackling the illumination variation challenge, we propose an illumination-robust framework using joint blind source separation (JBSS) and ensemble empirical mode decomposition (EEMD) to effectively evaluate HR from webcam videos. The framework takes the hypotheses that both facial ROI and background ROI have similar illumination variations. The background ROI is then considered as a noise reference sensor to denoise the facial signals by using the JBSS technique to extract the underlying illumination variation sources. Further, the reconstructed illumination-resisted green channel of the facial ROI is detrended and decomposed into a number of intrinsic mode functions using EEMD to estimate the HR. Experimental results demonstrated that the proposed framework could estimate HR more accurately than the state-of-the-art methods. The Bland-Altman plots showed that it led to better agreement with HR ground truth with the mean bias 1.15 beats/min (bpm), with 95% limits from -15.43 to 17.73 bpm, and the correlation coefficient 0.53. This study provides a promising solution for realistic noncontact and robust HR measurement applications.