We present a study of the local structure of high-pressure hydrogen around the liquid-liquid transition line based on results from the coupled electron-ion Monte Carlo method. We report results for the equation of state and for the radial distribution function between protons g(r) and results from a cluster analysis to detect the possible formation of stable molecular ions beyond the transition line as well as above the critical temperature. We discuss various estimates for the molecular fraction in both phases and show that, although the presence of H3+ ions is suggested by the form of the g(r), they are not stable against thermal fluctuations.