  We study untwisted heterobilayers of ferromagnetic and antiferromagnetic van
der Waals materials, with in particular a Dzyaloshinskii-Moriya interaction in
the ferromagnetic layer. A continuum low energy field theory is utilized to
study such systems. We develop a phase diagram as a function of the strength of
inter-layer exchange and Dzyaloshinskii-Moriya interactions, combining
perturbative and strong coupling analyses with numerical simulations using
Landau-Lifshitz-Gilbert equations. Various moir\'e-periodic commensurate phases
are found, and the commensurate-incommensurate transition is discussed. Among
the commensurate phases, we observe an interesting skyrmion lattice phase
wherein each moir\'e unit cell hosts one skyrmion.
