In this paper, we consider quotient structure and quotient difunctions in the context of interior and closure operators on textures in the sense of Dikranjan--Giuli. The generalizations of several results concerning separation and quotient mapping are presented. It is shown that the category of interior-closure spaces and bicontinuous difunctions has a $T_0$ reflection. Finally, we introduce some classes of quotient difunctions such as bi-initial and bi-final difunctions between interior-closure texture spaces.