The construction of millimeter-structured surface beams by superimposing scalar Bessel beams has proven to be a powerful technique for creating visual two-dimensional (2D) images in lossless media. In the present paper, we show that surface frozen waves can indeed be designed even in media having non-zero extinction ratios. Examples are provided for specific surface intensity patterns, revealing that our proposed solutions are promising candidates for a wide range of applications encompassing optical trapping displays, 2D and three-dimensional (3D) imaging and printing, nanochannel ablation in glass, optical trapping and manipulation of micro-sized particles and atoms, and so on.