Quantum materials whose atoms are arranged on a lattice of corner-sharing triangles, i.e., the kagome lattice, have recently emerged as a captivating platform for investigating exotic correlated and topological electronic phenomena. Here, we combine ultralow temperature angle-resolved photoemission spectroscopy (ARPES) with scanning tunneling microscopy and density functional theory calculations to reveal the fascinating electronic structure of the bilayer-distorted kagome material 𝐿⁢𝑛⁢Ti₃⁢Bi₄, where Ln stands for Nd and Yb. Distinct from other kagome materials, 𝐿⁢𝑛⁢Ti₃⁢Bi₄ exhibits twofold, rather than sixfold, symmetries, stemming from the distorted kagome lattice, which leads to a unique electronic structure. Combining experiment and theory we map out the electronic structure and discover double flat bands as well as multiple Van Hove singularities (VHSs), with one VHS exhibiting higher-order characteristics near the Fermi level. Notably, in the magnetic version NdTi₃⁢Bi₄, the ultralow base temperature ARPES measurements unveil an unconventional band splitting in the band dispersions which is induced by the ferromagnetic ordering. These findings reveal the potential of bilayer-distorted kagome metals 𝐿⁢𝑛⁢Ti₃⁢Bi₄ as a promising platform for exploring novel emergent phases of matter at the intersection of strong correlation and magnetism.