We introduce the notion of interlaced weak ditalgebras and apply reduction procedures to their module categories to prove a tame-wild dichotomy for the category F(Δ) of Δ-filtered modules for an arbitrary finite homological system (P,≤,{Δi}i∈P). This includes the case of standardly stratified algebras. Moreover, in the tame case, we show that given a fixed dimension d, for every d-dimensional indecomposable module M∈F(Δ), with the only possible exception of those lying in a finite number of isomorphism classes, the module M coincides with its Auslander-Reiten translate in F(Δ). Our proofs rely on the equivalence of F(Δ) with the module category of some special type of ditalgebra.