A detailed study of various two-particle correlation functions involving photons and neutral pions is presented in proton-proton and lead-lead collisions at the LHC energy. The aim is to use these correlation functions to quantify the effect of the medium (in lead-lead collisions) on the jet decay properties. The calculations are carried out at the leading order in QCD but the next-to-leading order corrections are also discussed. The competition between different production mechanisms makes the connection between the jet energy loss spectrum and the gamma-pi correlations somewhat indirect while the gamma-gamma correlations have a clearer relation to the jet fragmentation properties.