Photoproduction of πη-pairs from nucleons has been investigated from threshold up to incident photon energies of ≈ 1.4 GeV. The quasi-free reactions γp→pπ0η, γn→nπ0η, γp→nπ+η, and γn→pπ−η were for the first time measured from nucleons bound in the deuteron. The corresponding reactions from a free-proton target were also studied to investigate final-state interaction effects (for neutral pions the free-proton results could be compared to previous measurements; the γp→nπ+η reaction was measured for the first time). For the π0η final state coherent production via the γd→dπ0η reaction was also investigated. The experiments were performed at the tagged photon beam of the Mainz MAMI accelerator using an almost 4π coverage electromagnetic calorimeter composed of the Crystal Ball and TAPS detectors. The total cross sections for the four different final states obey the relation σ(pπ0η)≈σ(nπ0η)≈2σ(pπ−η)≈2σ(nπ+η) as expected for a dominant contribution from a Δ⋆→ηΔ(1232)→πηN reaction chain, which is also supported by the shapes of the invariant-mass distributions of nucleon–meson and π–η pairs. The experimental results are compared to the predictions from an isobar reaction model.