Large Pre-trained Language Models (PLMs) have become ubiquitous in the development of language understanding technology and lie at the heart of many artificial intelligence advances. While advances reported for English using PLMs are unprecedented, reported advances using PLMs for Hebrew are few and far between. The problem is twofold. First, so far, Hebrew resources for training large language models are not of the same magnitude as their English counterparts. Second, most benchmarks available to evaluate progress in Hebrew NLP require morphological boundaries which are not available in the output of standard PLMs. In this work we remedy both aspects. We present AlephBERT, a large PLM for Modern Hebrew, trained on larger vocabulary and a larger dataset than any Hebrew PLM before. Moreover, we introduce a novel neural architecture that recovers the morphological segments encoded in contextualized embedding vectors. Based on this new morphological component we offer an evaluation suite consisting of multiple tasks and benchmarks that cover sentence-level, word-level and sub-word level analyses. On all tasks, AlephBERT obtains state-of-the-art results beyond contemporary Hebrew baselines. We make our AlephBERT model, the morphological extraction model, and the Hebrew evaluation suite publicly available, for evaluating future Hebrew PLMs.