The deployment of Quantized Neural Networks (QNN) on advanced microcontrollers requires optimized software to exploit digital signal processing (DSP) extensions of modern instruction set architectures (ISA). As such, recent research proposed optimized libraries for QNNs (from 8-bit to 2-bit) such as CMSIS-NN and PULP-NN. This work presents an extension to the PULP-NN library targeting the acceleration of mixed-precision Deep Neural Networks, an emerging paradigm able to significantly shrink the memory footprint of deep neural networks with negligible accuracy loss. The library, composed of 27 kernels, one for each permutation of input feature maps, weights, and output feature maps precision (considering 8-bit, 4-bit and 2-bit), enables efficient inference of QNN on parallel ultra-low-power (PULP) clusters of RISC-V based processors, featuring the RV32IMCXpulpV2 ISA. The proposed solution, benchmarked on an 8-cores GAP-8 PULP cluster, reaches peak performance of 16 MACs/cycle on 8 cores, performing 21× to 25× faster than an STM32H7 (powered by an ARM Cortex M7 processor) with 15× to 21× better energy efficiency.