An evolutionary process is reflected in the sequence of changes through time of any trait (e.g. morphological, molecular). Yet, a better understanding of evolution would be procured by characterizing correlated evolution, or when two or more evolutionary processes interact. A wide range of parametric methods have previously been proposed to detect correlated evolution but they often require significant computing time as they rely on the estimation of many parameters. Here we propose a minimal likelihood framework modelling the joint evolution of two traits on a known phylogenetic tree. The type and strength of correlated evolution is characterized by few parameters tuning mutation rates of each trait and interdependencies between these rates. The framework can be applied to study any discrete trait or character ranging from nucleotide substitution to gain or loss of a biological function. More specifically, it can be used to 1) test for independence between two evolutionary processes, 2) identify the type of interaction between them and 3) estimate parameter values of the most likely model of interaction. In its current implementation, the method takes as input a phylogenetic tree together with mapped discrete evolutionary events on it and then maximizes the likelihood for one or several chosen scenarios. The strengths and limits of the method, as well as its relative power when compared to a few other methods, are assessed using both simulations and data from 16S rRNA sequences in a sample of 54 γ-enterobacteria. We show that even with datasets of less than 100 species, the method performs well in parameter estimation and in the selection of evolutionary scenario.