Heterostructures made of strongly correlated oxides host various fundamentally interesting and potentially useful emergent phenomena. ${(\mathrm{LaMn}{\mathrm{O}}_{3})}_{n}/{{(\mathrm{SrMn}{\mathrm{O}}_{3})}_{n}}_{\ensuremath{-}1}$ superlattices that consist of an $A$-type antiferromagnetic insulator $\mathrm{LaMn}{\mathrm{O}}_{3}$ and a $G$-type antiferromagnetic insulator $\mathrm{SrMn}{\mathrm{O}}_{3}$ were investigated in this work. Several very intriguing effects were observed in such superlattices that include (1) the coexistence of a strong exchange bias effect and a giant vertical magnetization shift in superlattices with intermediate periods, (2) an insulator-to-metal transition associated with a change in the superlattice thickness, and (3) a large nontrivial negative magnetoresistance around the insulator-to-metal transition. To understand these phenomena, microscopic preferential orbital occupancy in different superlattices was studied through measurements of x-ray linear dichroism at Mn $L$ edges. This study facilitated the construction of a spin configuration model that takes into account the competition between interfacial ferromagnetism and underlying canted antiferromagnetism in the superlattices and can successfully explain the observed novel magnetic and transport properties. The phase transition and giant vertical magnetization shift phenomena observed in this work offer additional degrees of freedom for applications of antiferromagnetic insulator manganite-based superlattices, enabling novel device concepts.