Negative samples have not been efficiently explored in multilingual dense passage retrieval. In this paper, we propose a novel multilingual dense passage retrieval framework, mHFN, to recover and utilize hard and false negative samples. mHFN consists of three key components: 1) a multilingual hard negative sample augmentation module that allows knowledge of indistinguishable passages to be shared across multiple languages and synthesizes new hard negative samples by interpolating representations of queries and existing hard negative samples, 2) a multilingual negative sample cache queue that stores negative samples from previous batches in each language to increase the number of multilingual negative samples used in training beyond the batch size limit, and 3) a lightweight adaptive false negative sample filter that uses generated pseudo labels to separate unlabeled false negative samples and converts them into positive passages in training. We evaluate mHFN on Mr. TyDi, a high-quality multilingual dense passage retrieval dataset covering eleven typologically diverse languages, and experimental results show that mHFN outperforms strong sparse, dense and hybrid baselines and achieves new state-of-the-art performance on all languages. Our source code is available at https://github.com/Magnetic2014/mHFN.