The laser interferometer space antenna (LISA) will produce a data stream containing a vast number of overlapping sources: from strong signals generated by the coalescence of massive black hole binary systems to much weaker radiation from sub-stellar mass compact binaries and extreme-mass ratio inspirals. It has been argued that the observation of weak signals could be hampered by the presence of loud ones and that they first need to be removed to allow such observations. Here we consider a different approach in which sources are studied simultaneously within the framework of Bayesian inference. We investigate the simplified case in which the LISA data stream contains radiation from a massive black hole binary system superimposed over a (weaker) quasi-monochromatic waveform generated by a white dwarf binary. We derive the posterior probability density function of the model parameters using an automatic reversible jump Markov chain Monte Carlo algorithm (RJMCMC) restricted to a single search model. We show that the information about the sources and noise are retrieved at the expected level of accuracy without the need to remove the stronger signal. Our analysis suggests that this approach is worth pursuing further and could be considered for actual analysis of the LISA data.