An analytical model is developed for the vertical coherence of the ambient noise field generated by a plane of sources at a finite depth beneath the ocean surface. To clarify the effects of source depth on the noise field, the relatively simple case of a semi-infinite ocean with an isovelocity profile is considered. The expression derived for the coherence is exact; it depends on the source depth explicitly, and it includes the homogeneous and inhomogeneous components of the field. When the sources are shallow, that is, the source depth is much less than a wavelength and the source–image pairs act as dipoles, the coherence is an oscillatory function of frequency, consistent with an earlier theory of noise coherence in deep water. With deeper sources, the dipole description fails and the coherence function becomes approximately independent of frequency. This change of character suggests that the spatial structure of the noise field at depth in the ocean could be inverted to yield information on the acoustic properties of the bubble sources associated with breaking surface waves.