Quasi-free photoproduction of $pieta$-pairs has been investigated from threshold up to incident photon energies of 1.4 GeV, respectively up to photon-nucleon invariant masses up to 1.9 GeV. Total cross sections, angular distributions, invariant-mass distributions of the $pieta$ and meson-nucleon pairs, and beam-helicity asymmetries have been measured for the reactions $gamma prightarrow ppi^0eta$, $gamma nrightarrow npi^0eta$, $gamma prightarrow npi^+eta$, and $gamma nrightarrow ppi^-eta$ from nucleons bound inside the deuteron. For the $gamma p$ initial state data for free protons have also been analyzed. Finally, the total cross sections for quasi-free production of $pi^0eta$ pairs from nucleons bound in $^3$He nuclei have been investigated in view of final state interaction (FSI) effects. The experiments were performed at the tagged photon beam facility of the Mainz MAMI accelerator using an almost $4pi$ covering electromagnetic calorimeter composed of the Crystal Ball and TAPS detectors. The shapes of all differential cross section data and the asymmetries are very similar for protons and neutrons and agree with the conjecture that the reactions are dominated by the sequential $Delta^{star}3/2^-rightarrowetaDelta(1232)rightarrowpieta N$ decay chain, mainly with $Delta(1700)3/2^-$ and $Delta(1940)3/2^-$. The ratios of the magnitude of the total cross sections also agree with this assumption. However, the absolute magnitudes of the cross sections are reduced by FSI effects with respect to free proton data.
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