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Stacking two semiconducting transition metal dichalcogenide (MX₂) monolayers to form a heterobilayer creates a new variety of semiconductor junction with unique optoelectronic features, such as hosting long-lived dipolar interlayer excitons. Despite many optical, transport, and theoretical studies, there have been few direct electronic structure measurements of these junctions. Here, we apply angle-resolved photoemission spectroscopy with micron-scale spatial resolution (µARPES) to determine the band alignments in MoSe₂/WSe₂heterobilayers, usingin-situelectrostatic gating to electron-dope and thus probe the conduction band edges. By comparing spectra from heterobilayers with opposite stacking orders, that is, with either MoSe₂or WSe₂on top, we confirm that the band alignment is type II, with the valence band maximum in the WSe₂and the conduction band minimum in the MoSe₂. The overall band gap isE_G= 1.43 ± 0.03 eV, and to within experimental uncertainty it is unaffected by electron doping. However, the offset between the WSe₂and MoSe₂valence bands clearly decreases with increasing electron doping, implying band renormalisation only in the MoSe₂, the layer in which the electrons accumulate. In contrast,µARPES spectra from a WS₂/MoSe₂heterobilayer indicate type I band alignment, with both band edges in the MoSe₂. These insights into the doping-dependent band alignments and gaps of MX₂heterobilayers will be useful for properly understanding and ultimately utilizing their optoelectronic properties.