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 326 pb(-1). Measurements were made for exchanged photon virtualities Q(2), in the range 10 to 350 GeV2. The photons were measured in the transverse-energy and pseudorapidity ranges 4 < E-T(gamma) < 15 GeV and -0.7 < eta(gamma) < 0.9, and the jets were measured in the transverse-energy and pseudorapidity ranges 2.5 < E-T(jet) < 35 GeV and -15< eta(jet) < 1.8. 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\%. (c) 2012 Elsevier B.V. All rights reserved.