Nulling interferometers such as Darwin or TPF will require a rather sophisticated data processing in order to perform a reliable planet detection and characterization. We propose a Bayesian method, which follows the maximum a posteriori (MAP) approach, to solve this problem. Our method accounts for the noise statistics and optimally combines the data from a nulling interferometer at all observed wavelengths to perform reliable planet detection. The problem to be solved is however multi-modal. We show how, in practice, the global optimum of the MAP criterion can be found by our method; the latter also provides the most likely spectral energy distributions of all planets. Additionally, we show that a proper regularization allows us to achieve an improved robustness of the detection and could lead to shorter observation times.