  The mirror P=W conjecture, formulated by Harder-Katzarkov-Przyjalkowski,
predicts a correspondence between weight and perverse filtrations in the
context of mirror symmetry. In this paper, we revisit this conjecture through
the lens of mirror symmetry for a Fano pair $(X,D)$, where $X$ is a smooth Fano
variety and $D$ is a simple normal crossing divisor. We introduce its mirror
object as a multi-potential analogue of a Landau-Ginzburg (LG) model, which we
call the hybrid LG model. This model is expected to capture the mirrors of all
irreducible components of $D$. We study the topological aspects, particularly
the perverse filtration, and the Hodge theory of hybrid LG models, building
upon the work of Katzarkov-Kontsevich-Pantev. As an application, we discover an
interesting upper bound on the multiplicativity of the perverse filtration for
a hybrid LG model. Additionally, we propose a relative version of the
homological mirror symmetry conjecture and explain how the mirror P=W
conjecture naturally emerges from it.
