The substantial memory bandwidth and computational demands of large language models (LLMs) present critical challenges for efficient inference. To tackle this, the literature has explored heterogeneous systems that combine neural processing units (NPUs) with DRAM-based processing-in-memory (PIM) for LLM acceleration. However, the high-precision PIM compute units incur significant area and power overhead in DRAM technology, limiting the effective computation throughput. In this paper, we introduce P3-LLM, a novel NPU-PIM integrated accelerator for edge LLM inference. Our approach is threefold: First, we propose a flexible mixed-precision quantization scheme, which leverages hybrid numerical formats to quantize different LLM operands with high compression efficiency and minimal accuracy loss. Second, we architect an efficient PIM accelerator for P3-LLM, featuring enhanced compute units to support hybrid numerical formats. Our careful choice of numerical formats allows to co-design low-precision PIM compute units that significantly boost the computation throughput under iso-area constraints. Third, we optimize the low-precision dataflow of different LLM modules by applying operator fusion to minimize the overhead of runtime dequantization. Evaluations on diverse LLMs and tasks demonstrate that P3-LLM achieves higher accuracy than state-of-the-art KV-cache quantization and weight-activation quantization algorithms. Combining the proposed quantization scheme with low-precision PIM architecture co-design, P3-LLM yields an average of $4.9\times$, $2.0\times$, and $3.4\times$ speedups over state-of-the-art LLM accelerators HBM-PIM, Ecco, and Pimba, respectively. Code is available at https://github.com/yc2367/P3-LLM.