We report powder and single-crystal neutron diffraction measurements of the magnetic order in $A{\mathrm{MnBi}}_{2}$ ($A=\mathrm{Sr}$ and Ca), two layered manganese pnictides with anisotropic Dirac fermions on a Bi square net. Both materials are found to order at ${T}_{\mathrm{N}}\ensuremath{\approx}300$ K in $\mathbf{k}=0$ antiferromagnetic structures, with ordered Mn moments at $T=10$ K of approximately $3.8 {\ensuremath{\mu}}_{\mathrm{B}}$ aligned along the $c$ axis. The magnetic structures are N\'eel type within the Mn-Bi layers, but the interlayer ordering is different, being antiferromagnetic in ${\mathrm{SrMnBi}}_{2}$ and ferromagnetic in ${\mathrm{CaMnBi}}_{2}$. This allows a mean-field coupling of the magnetic order to Bi electrons in ${\mathrm{CaMnBi}}_{2}$ but not in ${\mathrm{SrMnBi}}_{2}$. We find clear evidence that magnetic order influences electrical transport. First-principles calculations explain the experimental observations and suggest that the mechanism for different interlayer ordering in the two compounds is the competition between the antiferromagnetic superexchange and ferromagnetic double exchange carried by itinerant Bi electrons.