Multiword Expressions (MWEs) have been a bottleneck for Natural Language Understanding (NLU) and Natural Language Generation (NLG) tasks due to their idiomaticity, ambiguity, and non-compositionality. Bilingual parallel corpora introducing MWE annotations are very scarce which set another challenge for current Natural Language Processing (NLP) systems, especially in a multilingual setting. This work presents AlphaMWE-Arabic, an Arabic edition of the AlphaMWE parallel corpus with MWE annotations. We introduce how we created this corpus including machine translation (MT), post-editing, and annotations for both standard and dialectal varieties, i.e. Tunisian and Egyptian Arabic. We analyse the MT errors when they meet MWEs-related content, both quantitatively using the human-in-the-loop metric HOPE and qualitatively. We report the current state-of-the-art MT systems are far from reaching human parity performances. We expect our bilingual English-Arabic corpus will be an asset for multilingual research on MWEs such as translation and localisation, as well as for monolingual settings including the study of Arabic-specific lexicography and phrasal verbs on MWEs. Our corpus and experimental data are available at https://github.com/aaronlifenghan/AlphaMWE.