Multimodal alignment of histopathology encoders with transcriptomic and genomic data has been shown to significantly improve performance in downstream diagnostic tasks. Hematological cytology is unique in that visual single-cell evaluation is often paired with cytogenetics and molecular genetics for blood cancer diagnosis. In this study, we present a framework to align single white blood cell images with chromosomal aberrations (karyotype) and somatic mutations from targeted gene panels. Our training strategy follows a two-stage approach: (i) self-supervised, vision-only pretraining of a transformer aggregator using an iBOT head on a cohort of over 1500 patients, and (ii) genetic alignment via supervised contrastive loss on acute myeloid leukemia patients. Our genetically aligned patient encoder improves hematological diagnostic tasks, outperforming slide-level histopathology foundation models. Additionally, the model provides off-the-shelf retrieval capabilities for diseases and genetic alterations. Incorporating genetic data into patient encoders increases the quality of patient representations, providing a framework that aligns with clinical diagnostic workflows and paves the way for future multimodal hematology-specific AI. The code and model weights are available at https://github.com/marrlab/GenBloom.