Transitional discs are protoplanetary discs with opacity gaps/cavities in their dust distribution, a feature that may be linked to planet formation. We perform Bayesian modelling of the three transitional discs SZ Cha, CS Cha, and T25 including photometry from the Herschel Space Observatory to quantify the improvements added by these new data. We find disc dust masses between 2 x 10(-5) and 4 x 10(-4) M-circle dot and gap radii in the range of 7-18 au, with uncertainties of similar to one order of magnitude and similar to 4 au, respectively. Our results show that adding Herschel data can significantly improve these estimates with respect to mid-infrared data alone, which have roughly twice as large uncertainties on both disc mass and gap radius. We also find weak evidence for different density profiles with respect to full discs. These results open exciting new possibilities to study the distribution of disc masses for large samples of discs. ; National Science Foundation National Aeronautics and Space Administration