I present JEKYLL, a new code for modelling of supernovae (SN) spectra and lightcurves based on Monte-Carlo techniques for the radiative transfer. The code assumes spherical symmetry, homologous expansion and steady state for the matter, but is otherwise capable of solving the time-dependent radiative transfer problem in Non-Local-Thermodynamic-Equilibrium (NLTE). The method used was introduced in a series of papers by Lucy (2002,2003,2005), and has been extended and refined in several ways. Non-thermal excitation and ionization is included and calculated using the Spencer-Fano solver by Kozma et al. (1998). Macroscopic mixing of the material, known to occur in the SN explosion, is taken into account in a statistical sense using the method by Jerkstrand et al. (2011). We apply the code to Type IIb SNe by calculating the early (before 150 days) evolution for a model previously found to give a good match to SN 2011dh in the nebular phase. Comparing to observations, the early spectra and lightcurves of SN 2011dh are reasonably well reproduced, although there are also differences. In a broader context, most observational characteristics of Type IIb SNe, spectral as well as photometric, are well reproduced by the model. Comparing to results where NLTE was partly switched off, strong effects of NLTE are seen, even on the bolometric lightcurve. This highlights the need for full NLTE calculations when simulating the spectra and lightcurves of SNe.