It is generally accepted that the activities of the autonomic nervous system (ANS), which consists of the sympathetic (SNS) and parasympathetic nervous systems (PNS), are reflected in the low- (LF) and high-frequency (HF) bands in heart rate variability (HRV)—while, not without some controversy, the ratio of the powers in those frequency bands, the so called LF-HF ratio (LF/HF), has been used to quantify the degree of sympathovagal balance. Indeed, recent studies demonstrate that, in general: (i) sympathovagal balance cannot be accurately measured via the ratio of the LF- and HF- power bands; and (ii) the correspondence between the LF/HF ratio and the psychological and physiological state of a person is not unique. Since the standard LF/HF ratio provides only a single degree of freedom for the analysis of this 2D phenomenon, we propose a joint treatment of the LF and HF powers in HRV within a two-dimensional representation framework, thus providing the required degrees of freedom. By virtue of the proposed 2D representation, the restrictive assumption of the linear dependence between the activity of the autonomic nervous system (ANS) and the LF-HF frequency band powers is demonstrated to become unnecessary. The proposed analysis framework also opens up completely new possibilities for a more comprehensive and rigorous examination of HRV in relation to physical and mental states of an individual, and makes possible the categorization of different stress states based on HRV. In addition, based on instantaneous amplitudes of Hilbert-transformed LF- and HF-bands, a novel approach to estimate the markers of stress in HRV is proposed and is shown to improve the robustness to artifacts and irregularities, critical issues in real-world recordings. The proposed approach for resolving the ambiguities in the standard LF/HF-ratio analyses is verified over a number of real-world stress-invoking scenarios.