Incinerator bottom ash (IBA), a residue formed during the incineration of municipal solid waste, holds potential to be used as aggregate in civil engineering works. To contribute to a better understanding of the performance of IBA, this work studies the shear behaviour of interfaces between IBA and nonwoven geotextiles. To this end, inclined plane shear tests were carried out according to a standard procedure. For comparison, tests were also conducted with a natural aggregate (tout-venant). Interfaces with two different nonwoven geotextiles were tested. The geotextiles had the same mass per unit area (500 g/m2), but their other properties were notably different. The inclined plane shear behaviour of the aggregate—geotextile interfaces was evaluated under a constant vertical stress (10 kPa), using dry aggregates with a degree of compaction of 70%. The sliding mechanisms of the aggregates (IBA and tout-venant) over the geotextiles were examined and friction angles were estimated for the different aggregate–geotextile interfaces. The main findings of the work include: (1) changing the geotextile led to marked differences in the inclined plane shear behaviour of the aggregate–geotextile interfaces; and (2) the characteristics of the IBA–geotextile interfaces did not differ very markedly from those of the tout-venant–geotextile interfaces. For one geotextile, the friction angle tended to be slightly higher at the interface with IBA. In terms of friction behaviour with geotextiles (on sloped surfaces), IBA demonstrated to have potential as an alternative to the natural aggregate.