The present paper is a continuation of the study of the well known concept of bitopologieal quasi H-closed spaces fronj altogether new standpoints. Some interesting properties of such spaces are achieved via different approaches viz. covers, nets with well ordered sets as domains, θ-complete adherent points of sets, partial order relation and a few types of functions and multifunctions. These properties turn out to be new characterizations of almost regular bitopological spaces to be quasi H-closed. An application in the form of a fixed set theorem for a sort of multifunctions is also obtained for a bitopologieal quasi H-closed space.