BL Lacertae objects are extreme examples of Active Galactic Nuclei whose emission is almost purely nonthermal and whose spectrum is generally modelled as synchrotron emission up to an energy cutoff, above which Inverse Compton emission probably dominates. From studies of their multifrequency energy distribution, BL Lacs selected in the radio band are expected to have a spectral break in the mid to far-infrared band, a spectral region basically unexplored. We propose to study in a systematic manner the infrared spectrum of the only complete sample of radio-selected BL Lacertae objects, the 1 Jy sample, and fully exploit the sensitivity and large bandpass of ISO through multi-filter photometry between 3 and 180 microns with ISOCAM, ISOPHOT-P and ISOPHOT-C. This will allow us to search for the synchrotron break in the energy distribution of radio-selected BL Lacs, an important feature for the understanding of the detailed mechanisms of energy production and other puzzling characteristics of BL Lacs. We will also use the ISO observations for statistical studies, such as fill the infrared gap to complete the coverage of the spectral energy distribution of this unique and statistically well-defined sample, and derive the bivariate infrared and bolometric luminosity functions. Finally, our results will be compared with those obtained by a parallel proposal which will study the infrared properties of a sample of X-ray selected BL Lacs to gain insight into the intrinsic differences and/or similarities of the two classes.