Lead sulfide quantum dot solar cells have been largely studied only in the n-i-p architecture, with very few reports on the inverted p-i-n structure. Although the p-i-n structure provides several advantages, such as low-temperature processing and is generally compatible with tandem applications, the realization of p-i-n PbS solar cells has been hindered by the absence of suitable hole transport layers. That led to the necessity of introducing a 1,2-ethanedithiol (EDT) passivated PbS layer, which, while improving hole extraction, significantly hinders device reproducibility and stability. Here, we demonstrate PbS quantum dot solar cells based on carbazole- and dibenzothiophene-based self-assembled molecules as hole transport layers for the first time. We show that the properties of the organic interlayer influence the formation of the PbS quantum dot active layer and, consequently, the device performance. Among the studied self-assembled molecules, the best photovoltaic performance was obtained for Br-2EPT, reaching power conversion efficiencies of up to 6.3%, among the highest for p-i-n devices that are not based on the use of EDT-PbS. These results underline the great potential of self-assembled molecules as hole transport layers in inverted p-i-n PbS quantum dot solar cells.