This paper proposes a novel hybrid power-frequency multiple access (HPMA) framework for enabling successive interference cancellation (SIC)-free ambient backscatter communication in low-power Internet-of-Things (IoT) networks. Unlike conventional non-orthogonal multiple access (NOMA) systems that require SIC at receivers, the proposed HPMA design leverages both orthogonal and non-orthogonal subcarriers to allow multiple users to coherently combine their signals without interference cancellation. A passive backscatter device (BD) modulates information onto a carrier emitted by a base station, reflecting both user-specific and superposed signals to end users. We develop a unified analytical model under Nakagami-m fading and derive exact closed-form expressions for outage probability and throughput using the Meijer G-function. Asymptotic analysis further reveals the system’s diversity behavior and the impact of bandwidth and power allocation. Simulation results validate the theoretical findings and demonstrate that HPMA achieves significantly better performance than NOMA in terms of outage and throughput, especially in the low-to-moderate SNR regime. The proposed scheme offers a promising solution for SIC-free, energy-efficient, and spectrally efficient communication in large-scale IoT deployments.