Continuous monitoring of arterial blood pressure is clinically important for the diagnosis and management of cardiovascular diseases. Soft electronic devices with skin-like properties show promise in a wide range of applications, including the human-machine interface, the Internet of things, and health monitoring. Here, we report the use of add-on soft electronic interfaces to address the connection challenges between soft electrodes and rigid data acquisition circuitry for bioimpedance monitoring of cardiac signals, including heart rate and cuffless blood pressure. Nanocomposite films in add-on electrodes provide robust electrical and mechanical contact with the skin and the rigid circuitry. We demonstrate bioimpedance sensors composed of add-on electrodes for continuous blood pressure monitoring with high accuracy. Specifically, the bioimpedance collected with add-on nanocomposite electrodes shows a signal-to-noise ratio of 37.0 dB, higher than the ratio of 25.9 dB obtained with standard silver/silver chloride (Ag/AgCl gel) electrodes. Although the sample set is low, the continuously measured systolic and diastolic blood pressure offer accuracy of -2.0 6.3 mmHg and -4.3 3.9 mmHg, respectively, confirming the grade A performance based on the IEEE standard. These results show promise in bioimpedance measurements with add-on soft electrodes for cuffless blood pressure monitoring.