Spike train analysis generally focus on two purposes: (1) the estimate of the neuronal information quantity, and (2) the quantification of spikes or bursts synchronization. We introduce here a new multivariate index based on Lempel-Ziv complexity for spike train analysis. This index, called mutual Lempel-Ziv complexity (MLZC), can measure both spikes correlations and estimate the information quantity of spike trains (i.e. characterize the dynamic state). Using simulated spike trains from a Poisson process, we show that the MLZC is able to quantify spike correlations. In addition, using bursting activity generated by electrically coupled Hindmarsh-Rose neurons, the MLZC is able to quantify and characterize bursts synchronization, when classical measures fail.