The two-orbital double-exchange model is employed for the study of the magnetic and orbital orders in (RMnO3)n/(AMnO3)2n (R: rare earths; A: alkaline-earth metal) superlattices. The A-type antiferromagnetic order is observed in a broad region of parameter space for the case of SrTiO3 as substrate, in agreement with recent experiments and first-principles calculations using these superlattices. In addition, a C-type antiferromagnetic state is also predicted to be stabilized when using substrates like LaAlO3 with smaller lattice constants than SrTiO3, again in agreement with first-principles results. The physical mechanism for the stabilization of the A and C magnetic transitions is driven by the orbital splitting of the x2−y2 and 3z2−r2 orbitals. This splitting is induced by the Q3 mode of Jahn-Teller distortions created by the strain induced by the substrates. In addition to the special example of (LaMnO3)n/(SrMnO3)2n, our phase diagrams can be valuable for the case where the superlattices are prepared employing narrow bandwidth manganites. In particular, several nonhomogenous magnetic profiles are predicted to occur in narrow-bandwidth superlattices, highlighting the importance of carrying out investigations in this mostly unexplored area of research.