Isolated photon production in deep inelastic ep scattering has been measured with the ZEUS detector at HERA using an integrated luminosity of 320 pb−1. Measurements were made in the isolated-photon transverse-energy and pseudorapidity ranges 4<ETγ<15 GeV and −0.7<ηγ<0.9 for exchanged photon virtualities, Q2, in the range 10<Q2<350 GeV2 and for invariant masses of the hadronic system WX>5 GeV. Differential cross sections are presented for inclusive isolated photon production as functions of Q2, x, ETγ and ηγ. Leading-logarithm parton-shower Monte Carlo simulations and perturbative QCD predictions give a reasonable description of the data over most of the kinematic range.