The effect of a capacitive radio frequency (RF) substrate bias on the E-to H-mode transition and electron-heating dynamics in a low-pressure inductively coupled plasma (ICP) operated in hydrogen is investigated by phase-resolved optical emission spectroscopy (PROES) and Langmuir probe measurements. The inductive and capacitive power sources are driven at the same frequency and operated in a phase-locked mode with fixed but adjustable phase between them, as well as without a phase lock. For both operations, when the discharge is in the E-mode, the plasma density is significantly influenced by the choice of capacitive power. This directly affects the mode transition power: already low values of bias power can substantially reduce the threshold for the E-to H-mode transition. This coupling between both power sources is strongly dependent on the adjustable phase between them and is attributed to a phase-sensitive confinement mechanism for the highly energetic electrons produced by the expanding sheaths at the substrate and at the ICP coil. At higher pressures the beam electrons do not interact with the opposing sheath and, consequently, the effect diminishes. Using phase-unlocked operation reduces the overall beam confinement and also results in less pronounced coupling effects. In contrast, by using electrodes with ring-shaped trenches the initial energy of the beam electrons is enhanced, increasing the influence of the RF bias on the operation of the ICP discharge.