The HIV-1 envelope (Env) undergoes conformational changes during infection. Broadly neutralizing antibodies (bNAbs) are typically isolated by using soluble Env trimers, which do not capture all Env states. To address these limitations, we devised a vesicular stomatitis virus (VSV)-based probe to display membrane-embedded Env trimers and isolated five bNAbs from two chronically infected donors, M4008 and M1214. Donor B cell receptor (BCR) repertoires identified two bNAb lineages, M4008_N1 and M1214_N1, that class-switched to immunoglobulin G (IgG) and IgA. Variants of these bNAbs reconstituted as IgA demonstrated broadly neutralizing activity, and the IgA fraction of M1214 plasma conferred neutralization. M4008_N1 epitope mapping revealed a glycan-independent V3 epitope conferring tier 2 virus neutralization. A 4.86-Å-resolution cryogenic electron microscopy (cryo-EM) structure of M1214_N1 complexed with CH505 SOSIP revealed another elongated epitope, the V2V5 corridor, extending from V2 to V5. Overall, the VSVENV probe identified bNAb lineages with neutralizing IgG and IgA members targeting distinct sites of HIV-1 Env vulnerability.