In this work, we analyze brain-heart interactions during different mental states computing mutual information (MI) between the dynamic activity of different physiological systems. In 18 healthy subjects monitored in a relaxed resting state and during a mental arithmetic and a serious game task, multichannel EEG, one lead ECG, respiration and blood volume pulse were collected via wireless non-invasive biosensors. From these signals, synchronous 300-second time series were extracted measuring brain activity via the δ, θ, α, and β EEG power, and activity of the body district via the ECG R-R interval η, the respiratory amplitude ρ and the pulse arrival time π. MI was computed using a linear estimator: (i) between {η,ρ,π} and {δ,θ,α,β}, to measure overall brain-body interactions; (ii) between each time series and the others of the same district, to measure information shared within a district; and (iii) between each time series of a district and all series of the other district, to evaluate individual contributions to the information shared between brain and body. Results document the existence of statistically significant brain-body interactions, with high MI values involving mainly the η body dynamics and the δ and β brain dynamics. State-dependent variations were mostly relevant to the MI of the brain system involving δ, θ, α during mental arithmetic, and α and β during serious game. Thus, MI can be useful to detect correlated activity within and between brain and body systems monitored simultaneously during different mental states.