Seismocardiography (SCG) is a non-invasive method that can be used for cardiac activity monitoring. This paper presents a new electrocardiogram (ECG) independent approach for estimating heart rate (HR) during low and high lung volume (LLV and HLV, respectively) phases using SCG signals. In this study, SCG, ECG, and respiratory flow rate (RFR) signals were measured simultaneously in 7 healthy subjects. The lung volume information was calculated from the RFR and was used to group the SCG events into low and high lung-volume groups. LLV and HLV SCG events were then used to estimate the subjects HR as well as the HR during LLV and HLV in 3 different postural positions, namely supine, 45 degree heads-up, and sitting. The performance of the proposed algorithm was tested against the standard ECG measurements. Results showed that the HR estimations from the SCG and ECG signals were in a good agreement (bias of 0.08 bpm). All subjects were found to have a higher HR during HLV (HR$_\text{HLV}$) compared to LLV (HR$_\text{LLV}$) at all postural positions. The HR$_\text{HLV}$/HR$_\text{LLV}$ ratio was 1.11$\pm$0.07, 1.08$\pm$0.05, 1.09$\pm$0.04, and 1.09$\pm$0.04 (mean$\pm$SD) for supine, 45 degree-first trial, 45 degree-second trial, and sitting positions, respectively. This heart rate variability may be due, at least in part, to the well-known respiratory sinus arrhythmia. HR monitoring from SCG signals might be used in different clinical applications including wearable cardiac monitoring systems.