The production of isolated high-energy photons accompanied by jets has been measured in deep inelastic ep scattering with the ZEUS detector at HERA, using an integrated luminosity of . Measurements were made for exchanged photon virtualities, , in the range 10 to . The photons were measured in the transverse-energy and pseudorapidity ranges and , and the jets were measured in the transverse-energy and pseudorapidity ranges and . Differential cross sections are presented as functions of these quantities. Perturbative QCD predictions give a reasonable description of the shape of the measured cross sections over most of the kinematic range, but the absolute normalisation is typically in disagreement by 20–30%.