Results of angle-resolved electron spectroscopy of near-threshold photoionization of Ne atoms by combined femtosecond extreme ultraviolet and near infrared fields are presented. The dressed-electron spectra show an energetic distribution into so-called sidebands, being separated by the photon energy of the dressing laser. Surprisingly, for the low kinetic energy (few eV) sidebands, the photoelectron energy varies as a function of the emission angle. Such behavior has not yet been observed in sideband creation and has not been predicted in commonly used theoretical descriptions such as strong field approximation and soft photon approach. Describing the photoionization with a time-dependent Schrödinger equation allows a qualitative description of the observed effect, as well as the prediction of fine structure in the sideband distribution.