Alveospongia sinuosclera gen. nov. sp. nov. is described from shallow-waters off Canavieiras (Bahia, Brazil). The species bears an unusual morphology, combining saccular or alveolar, evenly perforated habit, and sinuous spiny microrhabdose microscleres. This sponge is tentatively classified within the Heteroxyidae Dendy (1905), on the basis of its confused choanosomal architecture of styles, and possession of spiny microrhabdose microscleres. Assays to generate DNA sequences from this material were unsuccessful. We emended the diagnosis of the family to include species bearing saccular/alveolar shape, microrhabdose acanthomicrostrongyles and styles/ strongyles with modifications at the ends. The proposed new genus is compared to the remaining heteroxyid genera, as well as Crella (Crellidae), Batzella (Chondropsidae), Goreauiella (Astroscleridae) and Sceptrintus (Podospongiidae). A revised key for identification of Heteroxyidae genera is provided.