Monoclonal antibodies (mAbs) targeting the influenza hemagglutinin (HA) have the potential to be used as prophylactics or templates for next-generation vaccines that provide broad protection. Here, we isolated broad, subtype-neutralizing mAbs from human B cells targeting the H1 or H3 HA head as well as a unique mAb targeting the stem. The H1 mAbs target the previously defined lateral patch epitope on H1 HAs and recognize HAs from 1933 to 2021 in addition to a swine H1N1 virus with pandemic potential. Using directed evolution, we improved the neutralization potency of these H1 mAbs towards a contemporary H1 strain. Using deep mutational scanning of four antigenically distinct H1N1 viruses, we identified potential viral escape pathways. For the H3 mAbs we used cryo-EM to define the targeted epitopes: one mAb recognizes the side of the H3 head, accommodating the N133 glycan and a pocket underneath the receptor binding site. The other H3 mAb recognizes an epitope in the HA stem that overlaps with previously characterized mAbs, but with distinct antibody variable genes and mode of recognition. Collectively, these mAbs identify common sites recognized by broad, subtype-specific mAbs that may be elicited by next-generation vaccines.